STATS: Classical Probability

subjective probability

a measure of the degree of belief that the event has occurred or will occur. (Guess or estimate

Classical probability

also called theoretical probability, is calculated by taking ALL possible outcomes for an experiment into account.

Decide if the following probability is classical, relative frequency, or subjective. At a local university, you poll a group of 140 students and find that 27 of them are from out-of-state.

relative frequency

Decide if the following probability is classical, relative frequency, or subjective. You calculate that the probability of randomly choosing a student who is left-handed is about 20%

relative frequency

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

sample space

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

sample space: ABV,ABR,ASV,ASR,MBV,MBR,MSV,MSR

Write out the sample space for the given experiment. Use the following letters to indicate each choice: B for blue, P for purple, O for orange, G for gray, T for teak, and M for maple. While renovating your house, you have a choice of paint colors for your game room: blue, purple, or orange. You also have the following options for the finish on your entertainment center: gray, teak, or maple.

sample space: BG,BT,BM,PG,PT,PM,OG,OT,OM

Write out the sample space for the given experiment. Use the letter H to indicate heads and T for tails. 2 coins are tossed.

sample space: HT,HH,TH,TT four outcomes possible

A coin is tossed 7 times. What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

1/128 Reason: sample space = 2^7 2 (H or T) tossed 7 times

A standard six-sided die is rolled. What is the probability of rolling a number greater than or equal to 4? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

1/2 reason: sample space= 6 (1,2,3,4,5,6) numbers greater than or equal to 4= 3 (4,5,6) 3/6 = 1/2

What is the probability of rolling a sum of 2 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.

1/36 reason: sample space= 36 (6 sided die * 6 sided die = 36 outcomes) sum 2= (1+1) only ONE way of getting a sum of 2 P(sum 2)= 1/36

There are 716 identical plastic chips numbered 1 through 716 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 560? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

1/716

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 a red on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places. purple 33 blue 44 red 34 green 43

17/77 Reason: total tosses= 154 red outcomes= 34 P(getting red)= 34/154 simplified= 17/77

There are 354 identical plastic chips numbered 1 through 354 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 211? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

35/59 reason: total chips= 354 chips less than 211= 210 (211-1) simplify 210/354 = 35/59

There are 105 identical plastic chips numbered 1 through 105 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

61/105 Reason: total chips= 105 chips greater than 44= (105-44) =61 P(chip>44)= 61/105

A box contains 95 red marbles, 58 white marbles, and 3 blue marbles. If a marble is randomly selected from the box, what is the probability that it is white or blue? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

61/156 reason: total marbles= 156 P(white marbles)= 58/156 P(blue marbles)= 3/156 **exclusive events bc there isn't blue AND white marbles** P(White OR Blue)= P(white) +P(blue) P(White OR Blue)= 58/156 + 3/156 = 61/156

relative frequency

calculated by dividing the number of times an event occurs by the total number of trials performed. (occurs in an experiment, NOT using all possible outcomes)

Decide if the following probability is classical, relative frequency, or subjective. Selecting a face card from a standard deck of cards.

classical probability

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

outcome

Decide if the following probability is classical, relative frequency, or subjective. You guess that there is a 30% chance that you will be assigned homework in your physics class on Monday.

subjective probability reason: "you GUESS"

You decide to record the hair colors of people leaving a lecture at your school. What is the probability that the next person who leaves the lecture will have red hair? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Blonde 37 Red 20 Brown 25 Black 42 Gray 39

20/163 reason; total= 163 red hair=20

What is the probability that a randomly selected person will have a birthday in December? 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.

31/365 reason: sample space= 365 days in the year Days in December= 31 31/365

You are going to play mini golf. A ball machine that contains 22 green golf balls, 18 red golf balls, 24 blue golf balls, and 25 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.

22/89 Reason: total balls= 89 green balls= 22