Deck 12: From Randomness to Probability

Question 1

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.
If 10% of the students have never taken a statistics class, 35% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that both of the first two groupmates you meet have studied at least one semester of statistics?

A)0.90
B)0.35
C)0.123
D)0.81
E)1.8

Answer 1

0.81

Question 2

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.
If 55% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied some statistics?

A)0.75
B)0.80
C)0.45
D)0.25
E)0.20

Answer 2

0.45

Question 3

Determine whether the events of rolling a fair die two times are disjoint, independent, both, or neither.

A)Disjoint
B)Independent
C)Both
D)Neither

Answer 3

Independent

Question 4

A survey of senior citizens at a doctor's office shows that 40% take blood pressure-lowering medication, 47% take cholesterol-lowering medication, and 13% take both medications.
What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?

A)1
B)0.6
C)0.74
D)0.87
E)0

Question 5

College students were given three choices of pizza toppings and asked to choose one
Favorite.The following table shows the results. $$\begin{array} { c | c c c c } \text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \\\hline \text { cheese } & 16 & 16 & 26 & 29 \\\text { meat } & 25 & 29 & 16 & 16 \\\text { vacois } & 16 & 16 & 25 &29\end{array}$$
Given that a student's favorite topping is meat, what is the probability that the student is a
Junior?

A)0.209
B)0.14
C)0.059
D)0.289
E)0.179

Question 6

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.

If 10% of the students have never taken a statistics class, 35% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that at least one of the first two groupmates you meet has studied more than one
Semester of statistics?

A)0.303
B)0.798
C)0.45
D)0.203
E)0.55

Question 7

For a person selected randomly from a certain population, events A and B are defined as follows.
A = event the person is male
B = event the person is a smoker
Find PA( or B).Round approximations to two decimal places.

A)0.4128
B)0.57
C)0.41
D)0.87
E)0.72

Question 8

College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results.
$$\begin{array} { c | c c c c } \text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \\\hline \text { cheese } & 16 & 16 & 26 & 29 \\\text { meat } & 25 & 29 & 16 & 16 \\\text { veggie } & 16 & 16 & 25 & 29\end{array}$$
Given that a student's favorite topping is veggie, what is the probability that the student is a junior or a senior?

A)0.208
B)0.380
C)0.385
D)0.41
E)0.631

Question 9

College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. $$\begin{array} { c | c c c c } \text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \\\hline \text { cheese } & 16 & 16 & 26 & 29 \\\text { meat } & 25 & 29 & 16 & 16 \\\text { veggie } & 16 & 16 & 25 & 29\end{array}$$
Find P(favorite topping is meat | student is junior).

A)0.239
B)0.16
C)0.186
D)0.301
E)0.062

Question 10

A survey revealed that 45% of people are entertained by reading books, 46% are entertained by watching TV, and 9% are entertained by both books and TV.What is the probability that a person will be entertained by either books or TV?

A)0.82
B)0.9
C)0.91
D)0.8
E) 1

Question 11

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective.If three of the products are randomly selected, find the probability that all of them are acceptable.

A)0.343
B)2.1
C)0.027
D)0.429
E)0.7

Question 12

In a blood testing procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative.If the probability that an individual sample tests positive is 0.12, what is the probability that the mixture will test positive?

A)0.528
B)0.0144
C)1.00
D)0.0000249
E)0.472

Question 13

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.
If 65% of the students have never taken a statistics class, 15% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied at least two semesters of statistics?

A)0.85
B)0.35
C)0.15
D)0.80
E)0.20

Question 14

At the track, a gambler bets on the wrong horse in a 10-horse field nine times in a row.Later, when talking to a friend, he said he was confident that he would pick the winner the next time, because he was "due to pick a winner." Comment on his reasoning.

A)If he doesn't pick the winning horse next time, he will shortly after that.
B)When there are 10 horses in a race and he has chosen the wrong horse nine times in a row, he statistically should pick a winner the next time.
C)This is false reasoning because there is no "law of averages" for independent events.
D)This is false reasoning because he doesn't appear to be lucky.
E)None of the above apply.

Question 15

In one city, 47.5% of adults are female, 10.2% of adults are left-handed, and 4.8% are females.For an adult selected at random from the city, let
F = event the person is female
L = event the person is left-handed.
Find P(F or L).Round approximations to three decimal places.

A)0.482
B)0.529
C)0.577
D)0.6245
E)0.679

Question 16

One ball is removed from a bag containing 1 blue ball, 1 red ball, 1 yellow ball, and 1 green ball.Without returning the first ball to the bag a second ball is removed.Determine whether the events are disjoint, independent, both, or neither.

A)Disjoint
B)Independent
C)Both
D)Neither

Question 17

The weather reporter predicts that there is a 20% chance of snow tomorrow for a certain region.What is meant by this phrase?

A)It will rain 20% of the day tomorrow.
B)The occurrence of snow is "truly random" and will occur 20% of the time.
C)20% of the time it snows on this date.
D)In circumstances "like this," snow occurs 20% of the time.
E)Snow occurs 20% of the time in this region.

Question 18

College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. $$\begin{array} { c | c c c c } \text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \\\hline \text { cheese } & 16 & 16 & 26 & 29 \\\text { meat } & 25 & 29 & 16 & 16 \\\text { veggie } & 16 & 16 & 25 & 29\end{array}$$
Find P(favorite topping is veggie | student is junior or senior).

A)0.316
B)0.46
C)0.359
D)0.605
E)0.197

Question 19

You roll a fair die five times.What is the probability that the numbers you roll are not all 3's?

A)0.9999
B)0.0001
C)0.833
D)0.402
E)0.598

Question 20

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.
If 35% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that neither of the first two groupmates you meet has studied any statistics?

A)0.35
B)0.70
C)0.65
D)0.123
E)0.40