MATH221 Week 2: Rules of Probability and Probability Analysis

A statistics class has 50 students and among those students, 42 are business majors and 8 like grilled cheese. Or the business majors, 7 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. - 0.86 - 0.94 - 0.98 - 0.84

-0.86

The probability of an event must fall between the values of _____ and _____. - 1, 10 - 0, 1 - 1, 10 - 1, 100

0, 1

Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a 4 and then selecting a 5. - 0.0059 - 0.0044 - 0.0769 - 0.0060

0.0059

Two cards are selecting with replacement from a standard deck of 52 cards. Find the probability of selecting a jack and then selecting a queen? - 0.0060 - 0.0769 - 0.00440 - 0.0059

0.0059

Two cards are selected without replacement from a standard deck of 52 cards. Find the probability of selecting a 4 and then selecting a 5. - 0.0059 - 0.0060 - 0.0044 - 0.0769

0.0060

Two cards are selected without replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond. - 0.0250 - 0.0625 - 0.0588 - 0.0637

0.0637

A random selection from a deck of cards selects one card. What is the probability of selecting an ace? - 0.50 - 0.077 - 0.250 - 0.025

0.077

You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first day and lose money on the next two days? - 0.216 - 0.144 - 0.096 - 0.288

0.096

You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first two days and lose money on the third day? - 0.216 - 0.144 - 0.096 - 0.288

0.144

A player succeeds at an action if a 9 or 10 is rolled. Assuming a fair d10, what is the probability of success?

0.2 since the d10 is fair, the probability of each number is equally likely. This P(1) = P(2) = ...= P(10) = 1/10 = 0.1 P(success) = P(9) + P(10) = 0.1 + 0.1 = 0.2

The probability of a golden retriever catching a tennis ball in mid-air is 74%. Find the probability that a golden retriever catches three tennis balls in mid-air? - 0.4052 - 0.5476 - 0.3889 - 0.0176

0.4052

The probabiilty of a golden retriever catching a tennis ball in mid-air is 78%. Find the probability that a golden retriever catches three tennis balls in mid-air. - 0.7878 - 0.6084 - 0.4746 - 0.4565

0.4746

A random number generator is used to select a number from 1 to 100. What is the probability of selecting an odd number? - 0.077 0.250 0.500 0.050

0.500

The probability of a golden retriever catching a tennis ball in mid-air is 81%. Find the probability that a golden retriever catches three tennis balls in mid-air. - 0.6561 - 0.4052 - 0.5119 - 0.5314

0.5314

A statistics class has 50 students and among those students, 35 are business majors and 7 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. - 0.84 - 0.78 - 0.80 - 0.72

0.78

What is the probability that the player fails? Type as #.#

0.8 The player fails if any number less than 9 is rolled. Eight such numbers can be rolled (1, 2, ...., 8) P(failure) = P(1) + P(2) + ... + P(8) = 8(0.1) = .08

A statistics class has 50 students and among those students, 35 are business majors and 8 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistics student is a business major or likes grilled cheese. - 0.80 - 0.94 - 0.84 - 0.96

0.80

An event is successful 1 out of every 5 attempts. What is the probability of the complement of that event? - 0.15 - 0.20 - cannot be determined - 0.80

0.80

Consider the table below: Age Group/Frequency 18-29/9831 30-39/7845 40-49/6869 50-59/6323 60-69/5410 70 and over/5279 What is the probability that the next person chosen will be in the 50-59 or 60-69 age groups? - 31.7% - 28.2% - 23.7% - 42.5%

28.2%

Consider the table below: Response (number of cats owned)/Frequency None/659 One/329 Two/52 Three/13 Four or more/8 What is the probability that the next person asked has only one cat? - 31% - 50% - 62% - 5%

31%

If there were 58 total products, 33 from company A and 25 from company B. If one of the 58 items is selected, what is the probability that it is from company A? - 25/58 - 25/33 - 58/33 - 33/58

33/58

Consider the table below. Production location/Correct/Defective/Total East/258/31/289 West/572/106/678 North/755/94/849 South/491/74/565 Total/2076/305/2381 Find the probability that a randomly selected product is from the West, given that it is defective. 34.8% 15.6% 84.4% 28.5%

34.8%

Consider the table below: Age Group/Frequency 18-29/9831 30-39/7845 40-49/6869 50-59/6323 60-69/5410 70 and over/5279 What is the probability that the next person chosen will be in the 30-39 or 40-49 age groups?

35.4%

Consider the table below. Production location/Correct/Defective/Total East/258/31/289 West/572/106/678 North/755/94/849 South/491/74/565 Total/2076/305/2381 Find the probability that a randomly selected product is from the North, given that it's is correct. 12.1% 87.2% 36.4% 88.9%

36.4%

Consider the table below: Age Group/Frequency 18-29/9831 30-39/7845 40-49/6869 50-59/6232 60-69/5410 70 and over/5279 What is the probability that the next person chosen will be in the 18-29 or 30-39 age groups? - 37.8% - 42.5% - 18.9% - 23.7%

42.5%

Consider the table below Response (number of cats owned)/Frequency None/659 One/329 Two/52 Three/13 Four or more/8 What is the probability that the next person asked has only two cats? - 5% - 62% - 50% -31%

5%

In a survey of 352 customers, 81 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor? - 5.30% - 5.24% - 22.8% - 23.01%

5.24%

Consider the table below: Urban or Rural/Profit/Loss/Total Urban location/50/38/88 Rural location/61/94/155 Total/111/132/243 Find the probability that a randomly selected location is in a rural location, given that it is profitable. - 45.7% - 48.8% - 51.4% - 55.0%

55.0%

Consider the table below: Urban or Rural/Profit/Loss/Total Urban location/50/38/88 Rural location/61/94/155 Total/111/132/243 Find the probability that a randomly selected location is going to be profitable, given that it is in an urban location. - 48.8% - 51.4% - 36.2% - 56.8%

56.8

Consider the table below: Age Group/Frequency 18-29/9831 30-39/7845 40-49/6869 50-59/6323 60-69/5410 70 and over/5279 What is the complement of P(30-49), or P(30-49')? - 76.3% - 18.9% - 64.6% - 35.4%

64.6%

Consider the table below: Age Group/Frequency 18-29/9831 30-39/7845 40-49/6869 50-59/6323 60-69/5410 70 and over/5279 What is the complement of P(50-69), or P(50-69')? - 71.8% 68.3% 64.6% 76.3%

71.8%

The event B is rolling less than a 3 on a six-sided die. B is best described as _______. - a simple event - a compound event - not an event

A compound event

The probability of an event given that another event has already occurred would be _____. - the same - a conditional probability - an independent probability - the complement of the event

A conditional probability

A card from a standard 52-card deck of playing cards is drawn. - A is the event of drawing a 5. B is the event of drawing a club. - A is the event of drawing a club. B is the event of drawing a black card. - A is the event of drawing a club. B is the event of drawing a spade.

A is the event of drawing a club. B is the event of drawing a spade. A card cannot belong to two different suits. Thus, A and B are mutually exclusive.

A 6-sided die is rolled. - A is the event of rolling a number less than 5. B is the event of rolling a number greater than 3. - A is the event of rolling a number greater than 5. B is the event of rolling a number less than 3. - A is the event of rolling an even number. B is the event of rolling a prime number.

A is the event of rolling a number greater than 5. B is the event of rolling a number less than 3. A number cannot be both greater than 5 and less than 3. Thus A and B are mutually exclusive.

A coin is flipped five times. Ex. HTHTH means that the five flips are head, tails, heads, tails, and heads, in that order. - A is the even that the first flip comes up heads. B is the event that the last flip comes up tails. - A is the event that the first two flips come up heads. B is the event that the last two flips come up tails. - A is the event that the first three flips come up heads. B is the event that the last three flips come up tails.

A is the event that the first three flips come up heads. B is the event that the last three flips come up tails. The third flip is part of both the first three flips and the last three flips. No outcome is possible where the third flip is both heads and tails at the same time. Thus, A and B are mutually exclusive.

Probability

A measure of how likely an event is to occur; the number of desired outcomes divided by the total number of outcomes in the sample space, assuming that all outcomes are equally likely; the relative frequency of the desired outcome, or the proportion of times the outcome will occur when an experiment is repeated an infinite number of times.

Experiment

A procedure that results in one out of a number of possible outcomes.

Event

A subset of the sample space

Compound event

A subset of the sample space consisting of more than one outcome.

Simple event

A subset with a single outcome

A 6-sided die is rolled and the number of dots displayed is recorded. Is the roll of the die an experiment or an outcome? - an experiment - an outcome

An experiment

A 6-sided die is rolled and the number of dots displayed is recorded. 4 dots are displayed. Is the 4 dots being displayed an experiment or an outcome?

An outcome

Which of the following would be defined as one minus the probability of an event? - discrete probability - Complement of an event - combination - conditional probability

Complement of an event

The probability of a team winning its next game is 48%. The probability of losing its next game would be called the: - multiplication rule - complement of winning - empirical rule - conditional probability

Complement of winning

Classify these events. A study found that people who suffer from stress are more likely to have health issues. These events would be considered: - Subjective - Classical - Independent - Dependent

Dependent

Classify these events. Selecting a king from a deck of cards, keeping it and selecting a queen from the same deck. These events would be considered: - Dependent - Empirical - Independent - Subjective

Dependent

Classify these events. Some businesses have large stores and some businesses have large parking lots. These events would be considered: - Independent - Subjective - Classical - Dependent

Dependent

P(A) = 0.3 P(B) = 0.3 A and B are mutually exclusive events. - Independent - Dependent

Dependent {Since and B are mutually exclusive, P(A∩B)=0 and P(A|B)=0. Since P(A|B)≠P(A), A and B are dependent.}

P(A|B) = 0.3 P(B) = 0.6 P(A) = 0.5 - Independent - dependent

Dependent {since P(A|B) ≠ P(A), A and B are dependent.}

Two cards are drawn from the same deck of cards. The first card is not put back into the deck after being drawn. A is the event of drawing a red card on the first draw. B is the event of drawing a red card on the second draw. - independent events - dependent events

Dependent events (Since a card is removed from the deck after the first draw, the second draw has a different probability of drawing a red card. Thus, A and B are dependent events.)

Based on past experience, it is estimated that a restaurant will serve 122 guests on a weekday evening. This is an example of which type of probability? - empirical probability - public probability - classical probability - subjective probability

Empirical probability

A "low" calorie expenditure defined as fewer than 800 calories. - experiment - sample space - event - outcome

Event

Placing a calorie messing device on a child for a day and then reading the device value. - experiment - sample space - event - outcome

Event

Multiplication rule

Gives the probability of 2 independent events happening together. Let A and B be independent events. The probability that both A and B occur is P (A and B) = P(A)P(B)

Mutually exclusive

Have no outcomes in common; Events are represented by non-overlapping circles in a Venn diagram.

Classify these events. Selecting a king from a deck of cards, replacing it and selecting a queen from the same deck. These events would be considered: - Empirical - Subjective - Dependent - Independent

Independent

Classify these events. Selecting a king from a deck of cards, replacing it and selecting another king from the same deck. These events would be considered: - Empirical - Subjective - Dependent - Independent

Independent

If the occurrence of one event does not affect the probability of another event, then those events are _____. - independent - mutually exclusive - discrete - continuous

Independent

P(A|B) = 0.3 P(B) = 0.8 P(A) = 0.3 - independent - dependent

Independent {Since P(A|B) = P(A), A and B are independent}

P(B|A) = 0.8 P(B) = 0.8 P(A) = 0.3 - independent - dependent

Independent {Since P(B|A) = P(B), and A and B are independent}

Two cards are drawn from the same deck of cards. The first card is put back into the deck after being drawn. A is the event of drawing a red card on the first draw. B is the event of drawing a red card on the second draw. - independent events - dependent events

Independent events (Since the first card is returned to the deck after being drawn, the second card is drawn from the same deck as the first card was, and the probabilities do not change. Thus, A and B are independent events.)

One card is drawn from each of two decks of cards. A is the event of drawing a red card from the first deck. B is the event of drawing a red card from the second deck. - independent events - dependent events

Independent events (Since the two decks are separate, drawing a red card from one deck does not affect the probability of drawing a red card in the other deck, and vice versa. Thus, A and B are independent events.)

Randomly select a customer that lives in a retirement home. Randomly select a customer that is a teenager. Are these events mutually exclusive?

Mutually exclusive

Two events that cannot occur at the same time would be considered _______ events. - continuous - independent - mutually exclusive - discrete

Mutually exclusive

Randomly select a customer that takes the bus to our store. Randomly select a customer that drove to our store. Are these events mutually exclusive?

Mutually exclusive events

An experiment involves flipping two coins. Two coins are flipped, and the outcome HT is observed. Is the sample space {H, T}?

No

An experiment of rolling a die is repeated 3 times. The experiments result in the 3 outcomes 2, 4, and 5. Do the three outcomes represent the sample space?

No

Noah conducts an experiment by flipping a coin twice. The sample space for this experiment is {HH, HT, TH, TT}. Which of the following is a simple event? - Noah flips two heads. - Noah flips one heads and one tails. - Since Noah is flipping the coin twice, no simple events can exist.

Noah flips two heads.

Randomly select a customer that takes the bus to our store. Randomly select a customer that I a teenager. Are these events mutually exclusive?

Non-mutually exclusive

A gym teacher defines an experiment to be running a mile race three times in gym class. Sue runs the mile three times. Sue's fastest time was 6:10. This time can best be described as _____. - a simple event - a compound event - not an event

Not an event

1200 - experiment - sample space - event - outcome

Outcome

If two events are mutually exclusive, then we know that _____ - P(A and B) = 0 - P(A or B) = 0 - P(B|A) = P(B) - P(B|A) = P(A)

P(A and B) = 0

The multiplication rule is used to find the probability of ______. - P(A|B) - P(A or B) - P(A and B) - P(A*B)

P(A or B)

If two events are independent, then we know that _____. - P(A or B) = 0 - P(B|A) = P(B) - (P(B|A) = P(A) - P(A and B) = 0

P(B|A) = P(B)

Complement rule

Relates the probability of an event to the probability of the complement of the event.

Outcome

Result of an experiment

1, 2, 3, ...., 4999, 5000 - experiment - sample space - event - outcome

Sample space

Based on the CEO's perception, a company estimates that a new product will be purchased by 32% of current customers. This is an example of f which type of probability? - Classical probability - public probability - empirical probability - subjective probability

Subjective probability

Empty set

The event consisting of no outcomes.

Sample space

The set of all possible outcomes

Vein diagram

Visually represents a sample space and sets of events in the sample space; the sample space is represented by a rectangle. Every outcome appears inside the rectangle. An event is represented by a circle enclosing the outcomes in that event. Events with outcomes in common are represented as overlapping circles.

A 6-sided die is rolled. Is the sample space {1, 2, 3, 4, 5, 6}?

Yes

An experiment involves flipping two coins. Two coins are flipped, and heads is observed on the first coin and tails on the second coin, represented as HT. Is HT an outcome of this experiment?

Yes

You flip a coin 3 times. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Which of the following is a compound event? - You get exactly 3 heads - You get exactly 2 tails - You get exactly 3 tails - This is not an event

You get exactly 2 tails