Bus Stat Ch 4

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The newly elected president needs to decide the remaining 4 spots available in the cabinet he/she is appointing. If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

See screenshot = 24,024

Decide if the following probability is classical, empirical, or subjective. You calculate that the probability of randomly choosing a student who is living in the dorms is about 43%

empirical

Decide if the following probability is classical, empirical, or subjective. You calculate that the probability of randomly choosing a student who is from out-of-state is about 51%

it is empirical probability as it can be calculated based on observed frequency of out of state students divided by total students.

The set of all possible outcomes for a given probability experiment is called the

sampie space

A coin is tossed 8 times. What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

total sample space = 28 = 256 sample space for getting all heads= 1 So, P(getting all heads) = 1 / 256 = 0.0039 (ans)

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 4 types of drinks to choose from, 4 types of sandwiches, and 3 types of chips. How many different value meal packages are possible?

ypes of drinks = 4 types of snadwich = 6 types of chips = 3 Total number of different meal packages possible = 4 * 4 * 3 = 48 (ans)

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 8 Pennies, 22 Dimes, 15 Nickels, 12 Quarters what is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a quarter? Express your answer as a fraction or a decimal number rounded to four decimal places.

# of quarters (12/56) X (15/56) nickels / Total coins

Decide if the following probability is classical, empirical, or subjective. You believe you have a 1/13 chance of drawing a 6 from a standard deck of cards.

Classical

Each individual result of a probability experiment is called a(n)

Outcome

The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. What is the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to 4 decimal places, if necessary.

- The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. What is the probability that the next fish caught is a drum or a bluefish? Enter a fraction or round your answer to 4 decimal places, if necessary. - Drum and flounder / total # fish = .6472

The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing. If there are 12 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed

1320 Explanation: 12! / (12 - 3)!

Out of 423 applicants for a job, 229 have over 10 years of experience and 62 have over 10 years of experience and have a graduate degree. Consider that 133 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree?

133/229

A doctor visits her patients during morning rounds. In how many ways can the doctor visit 6 patients during the morning rounds?

6*5*4*3*2*1 = 720

You are using a local home remodeling company to remodel your kitchen. They have 8 different cabinet door styles, 15 countertop choices, and 13 different types of flooring. How many different kitchen remodels could be done using these material choices?

8X15X13= 1560

A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different lineups are possible?

See screenshot for excel formula and see saved png

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 14 Pennies 20 Dimes 14 Nickels 29 Quarters

Total coins = 14 + 20 + 14+ 29 = 77 P(picking quarter first and then a nickel) = 29/77 * 14/76 = .0694

You are going to play mini golf. A ball machine that contains 23 green golf balls, 24 red golf balls, 24 blue golf balls, and 22 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a green golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Total number of valls = 23 + 24 + 17 + 25 = 89 Number of yellow balls = 25 So, P (Getting yellow golf ball) = 23/93 or .2473

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a jack and then, without replacement, another jack?

Use conditional probability for dependent events since the cards are drawn without replacement. Recall that a standard deck of 52 cards has 4 jacks.A jack was already drawn, so that leaves us with 51 cards in the deck. Since a jack was already drawn, that leaves us with 3 jacks in the deck. Then applying the conditional probability rules, the probability of drawing a jack, given the first card drawn was also a jack, is = 3/51 = 1/17 ≈0.0588

A box contains 11 green marbles and 7 white marbles. If the first marble chosen was a green marble, what is the probability of choosing, without replacement, a white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.

Use conditional probability for dependent events since the marbles are drawn without replacement. Recall that we were given 11 green marbles and 7 white marbles. This will give us a total of 18 marbles. A green marble was drawn first, which takes one marble away from the total marbles ( 18−1=17). Of course the number of white marbles remains the same. Therefore, applying the conditional probability rules, the probability of choosing a white marble after the first marble chosen was green is P(white|||green)=7/17≈0.4118

Describe the complement of the given event. 74% of a person's credit card purchases are ninety dollars or more.

A= Event credit card purchases P(A)=.74 Complement of given event A is: P(A^c)= 1 - P (A) =1 - .74 =.26

Determine whether the following events are mutually exclusive. Choosing a heart or a club out of a standard deck of cards.

Mutually exclusive. Choosing a red card or a club out of standard deck cannot occur at same time.

Evaluate: 7!/4!(7−4)!

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Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for asparagus, E for eggs, S for shrimp, V for vinaigrette, and H for honey mustard

The sample space is given below. S = { MEV, MEH, MSV, MSH, AEV, AEH, ASV, ASH } The total number of sample points is 8

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a spade for the second card drawn, if the first card, drawn without replacement, was a diamond? Express your answer as a fraction or a decimal number rounded to four decimal places.

Use conditional probability for dependent events since the cards are drawn without replacement. Recall that a standard deck of 52 cards has 13 diamonds and 13 spades.A diamond was already drawn, so that leaves us with 51 cards in the deck. Since a diamond is not a spade, we are left with 13 spades in the deck. =13/51

You are using a local home remodeling company to remodel your kitchen. They have 18 different cabinet door styles, 15 countertop choices, and 11 different types of flooring. How many different kitchen remodels could be done using these material choices?

Number of different kitchen remodels that could be done using these material choices = 18* 15 *11= 2970

Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, A for asparagus, S for shrimp, T for turkey, V for vinaigrette, and I for Italian. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, asparagus. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: vinaigrette, Italian.

OSV,ASV,OTV,OSI,ATV,ASI,OAI,OAV

On a six-day vacation, the forecast is an 80% chance of rain every day. What's the probability that it rains every day? Enter a fraction or round your answer to 4 decimal places, if necessary.

= (80/100)^6 = ≈0.2621

Determine whether the following events are mutually exclusive. Choosing a student who is a physics major or a chemistry major from a nearby university to participate in a research study. (Assume that each student only has one major.)

Assumption is each student has only one major. Therefore, no students has both the majors. So, probability that the students has both major is zero. That is P(A and B) = 0 Therefore, The events are mutually exclusive.

There are 789 identical plastic chips numbered 1 through 789 in a box. - What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 522 ? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Correct Answer:521/789 or 0.6603

A person tosses a coin 12 times. In how many ways can he get 11 heads?

Flipping a fair coin fairly, 12 times, offers the possibility of 2^12 = 4,096 outcomes.The number of outcomes with 11 heads = 12!/(1!)(11!) = 12.

In how many ways can the letters in the word 'Alaska' be arranged?

If we treat each letter as distinct, we get 6!=720. However, the letter 'a' is repeated three times, so we must divide by 3! to get 120 distinct arrangements.

Determine whether the following value could be a probability. 23/15

No, because a valid probability value ranges between 0 and 1 (inclusive), and this given fraction is greater than 1 in value.

A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2183 class attendees. The data is summarized in the table below.

- Then, the probability that an attendee does not attend a barre class is calculated as follows. P(not attending barre)= 1 − P(attending barre)= 1 − 479/2183=1704/2183≈0.7806 So take total attending and not attending / total # class attendants. Then subtract 1 (but use positive instead of negative)

There are 12 people in an office with 4 different phone lines. If all the lines begin to ring at once, how many groups of 4 people can answer these lines?

See screenshot and saved png

A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of each type of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtain either a dime or a penny? Enter a fraction or round your answer to 4 decimal places, if necessary.

Dime or penny chances / total coins = .56

Write out the sample space for the given experiment. Use the letter H to indicate heads and T for tails. 3 coins are tossed.

-The possible outcomes of a single coin toss is either head or tail. - Hence, the sample space for a single coin toss can be defined as: S={H,T}S = \left\{ {H,T} \right\}S={H,T} - Here, H stands for observing the head on the toss of a coin and T stands for observing the tail on the toss of a coin. - Here, HH stands for observing the head on both coin toss, HT stands for observing the head on first toss and tail on second toss, TH stands for observing the tail on first toss and head on second toss and TT stands for observing the tail on both tosses of a coin. Answer: The sample space for observing the three coin toss is {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

What is the probability that a randomly selected person will have a birthday in May? Assume that this person was not born in a leap year. Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Number of days in May = 31 Total number of days = 365 Hence, P(Birthday in May) = 31/365 or 0.0849

You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

This means that there are 128 options (2^7), and 21 ways to have 2 toppings. 21/128

There are 251 identical plastic chips numbered 1 through 251 in a box. - What is the probability of reaching into the box and randomly drawing the chip numbered 171? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Probability is the likelihood or chance of an event occurring. Probability can be determined using the formula below - Since there is only one chip numbered 674 in the box, n(E)=1. Since there are a total of 862 chips in the box = 1/862

A telemarketer's computer selects phone numbers at random. The telemarketer has recorded the number of respondents in each age bracket for one evening in the following table. What is the probability that the next respondent will be between

Solution: Proportion of class = frequency of class / total frequency Total frequency: 196. There were 21+32=53 respondents that are between 18 and 35 and 28+21+32+60+55=196 respondents in total. The probability that the next respondent will be between 18 and 35 is then calculated as follows. P(between 18 and 35)=53/196≈0.2704

Evaluate: 13p8

The expression given is a permutation. Remember that a permutation is used when order is important. Written symbolically: nPr =n!/(n−r)! Therefore we can simplify this expression P813=13!(13−8)!=13!5!=6,227,020,800120=51,891,840 *n! = factorial n! means = 1⋅2⋅3⋅...⋅n 5! = 1⋅2⋅3⋅4⋅5 = 120

Find the number of outcomes in the complement of the given event. Out of 270 apartments in a complex, 174 are subleased.

270 - 174

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll an orange on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answer: orange/ total

Out of 423 applicants for a job, 229 have over 10 years of experience and 62 have over 10 years of experience and have a graduate degree. What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience? Enter a fraction or round your answer to 4 decimal places, if necessary.

Probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree = (Number of applicants with over 10 years experience and a graduate degree) / ( Number of applicant with a graduate degree) =62 / 229

Decide if the following probability is classical, empirical, or subjective. You believe that you have an 8% chance of getting into an accident on your way to the movies.

Subjective - This is solely based on the intuition of a person. It is vague and rarely accurate

There are 28 different colored pencils in a box. What is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement? Enter a fraction or round your answer to 4 decimal places, if necessary.

1/28 X 1/27 = .0013

A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 11? Express your answer as a fraction or a decimal number rounded to four decimal places.

Let P(x) be the probability of rolling the sum x with a standard pair of dice. For example, P(5)=4/36 since the probability of rolling a 5 with a pair of dice is 4/36. (Recall that there are 4 ways to roll a 5 and 36 total outcomes possible when rolling a pair of dice.) Because it is impossible to roll two different sums at the same time (e.g., one cannot roll a 7 and simultaneously roll a 10), the solution to this problem is obtained by applying the addition rule for mutually exclusive events and summing up the probabilities for rolling sums greater than or equal to 11. This can all be done simply by computing the value of P(x) for each sum greater than or equal to 11 on up to the sum 12 (you cannot roll a sum greater than 12 of course!) and then adding up these computations. Addition Rule for Mutually Exclusive Events If two events, E and F, are mutually exclusive, then P(EorF)=P(E)+P(F)

Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 6 people, and there are 6 different possible weapons and 9 possible rooms. At one point in the game, you have narrowed the possibilities down to 3 people, 3 weapons, and 6 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct?

= (1/3*(1/3)*(1/6) = .0185

What is the probability of rolling a sum of 11 on a standard pair of six-sided dice? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.

Sample space = {(1,1), (1,2), (1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), (3,1),(3,2), (3,3),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} - Getting a sum of = { (6,5) (5,6) } = 2 - Probability of getting a sum of 11 = 2/36 = 1/18 = 0.05556

A box contains 14 large marbles and 10 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green?

Count the number of marbles which are either large or green and then use the classical probability formula. (The Addition Rule can be used to solve this problem, but a quick counting of the marbles will yield the solution more efficiently.) We're interested in counting up all the marbles that are either large or green (or perhaps both). Now, we're told that there are 14 large marbles. The only other marbles of interest, then, are small marbles which are green. Since 3 of the 10 small marbles are white, we know that 10−3=7 of the small marbles are green. Therefore, the total number of marbles that are large or green is 14+7=21. Finally, we know that the box contains a grand total of 14+10=24 marbles. So, the probability that a randomly selected marble will be large or green is 21/24=7/8=0.8750

A box contains 16 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green?

Count the number of marbles which are either small or green and then use the classical probability formula. (The Addition Rule can be used to solve this problem, but a quick counting of the marbles will yield the solution more efficiently.) We're interested in counting up all the marbles that are either small or green (or perhaps both). Now, we're told that there are 18 small marbles. The only other marbles of interest, then, are large marbles which are green, and there are 9 of these. Therefore the total number of marbles that are small or green is 18+9=27. Finally, we know that the box contains a grand total of 16+18=34 marbles. So, the probability that a randomly selected marble will be small or green is 27/34≈0.7941

A standard six-sided die is rolled. What is the probability of rolling a number less than 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

When a die is rolled, here it's Total possible outcome is= 6 and sample space is = 2 ( i.e. 1 & 2) - Probability of getting less than 3 = 2/6 =1/3

You need to have a password with 4 letters followed by 3 even digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your password?

See png For this type of problem, we will use the Permutation Rule.The task is to select a password with 4 letters followed by 3 even digits. We can take the viewpoint that there are essentially two tasks being performed, namely, determining the alphabetical portion of the password and determining the numerical portion of the password. For the alphabetical part, 4 letters are being chosen from a group of 26 letters, and for the numerical part, 3 numbers are being chosen from a group of 5 even digits. In both the alphabetical portion and numerical portion of the password, order matters as it does with passwords and codes in general.

On a seven-day vacation, the forecast is a 65% chance of rain every day. What's the probability that it rains every day?

Given there is 65% chance of rain everyday(on any day of 7 days ) - probability of rain on any particular day is 0.65 then by multiplication theorem of independent events , probability of raining everyday will be (0.65) × (0.65) × .....×(0.65) , ( 7 times multiplication of 0.65 ) = 0.0490 up to 4 decimal places.