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1 A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely? (i) H T H

1

A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely?

(i)

H T H T H T H T H T H T

(ii)

H T T H H T T H T H H T

(iii)

H H H H H H H H H H H H

(iv)

T T T H T H H H H T H H

  1. (ii) because there are an equal number of heads and tails but in a random order
  2. (i) because there are an equal number of heads and tails.
  3. (iv) because you won't necessarily get the same number of heads and tails with a fair coin
  4. They are all equally likely.
  5. (iii) because heads are just as likely as tails
Question 2

In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population.

Let A represent the event "the first individual has diabetes."

Let B represent the event "the second individual has diabetes."

True or false? A and B are independent events.

  1. True
  2. False
Question 3

For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.89 independently of the others.

The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least oneof the 3 systems will detect it?

Your answer should be rounded to 5 decimal places.

Question 4

In a certain liberal arts college with about 10,000 students, 57% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?

Your answer should be rounded to 4 decimal places.

Question 5

According to the information that comes with a certain prescription drug, when taking this drug, there is a 17% chance of experiencing nausea (N) and a 45% chance of experiencing decreased sexual drive (D). The information also states that there is a 10% chance of experiencing both side effects.

What is the probability of experiencing only nausea?

Your answer should be rounded to two decimal places.

Question 6

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.

What is the probability of experiencing neither of the side effects?

Your answer should be to two decimal places.

Question 7

According to the information that comes with a certain prescription drug, when taking this drug, there is a 24% chance of experiencing nausea (N) and a 42% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.

What is the probability of experiencing nausea or a decrease in sexual drive?

Your answer should be rounded to 2 decimal places.

Question 8

An engineering school reports that 51% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 32% are both male and between the ages of 18 and 20.

What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?

Your answer should be to two decimal places.

Question 9

An engineering school reports that 58% of its students were male (M), 37% of its students were between the ages of 18 and 20 (A), and that 23% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).

Your answer should be given to two decimal places.

Question 10

An engineering school reports that 53% of its students were male (M), 30% of its students were between the ages of 18 and 20 (A), and that 23% were both male and between the ages of 18 and 20.

What is the probability of a random student being male or between the ages of 18 and 20?

Your answer should be rounded to two decimal places.

Question 11

Let A and B be two independent events such that P(A) = 0.47 and P(B) = 0.43.

What is P(A or B)?

Your answer should be given to 4 decimal places.

Question 12

Let A and B be two independent events such that P(A) = 0.2 and P(B) = 0.7.

What is P(A and B)?

Your answer should be given to 2 decimal places.

Question 13

Let A and B be two disjoint events such that P(A) = 0.52 and P(B) = 0.2.

What is P(A and B)?

Question 14

Let A and B be two disjoint events such that P(A) = 0.28 and P(B) = 0.52.

What is P(A or B)?

Question 15

The following probabilities are based on data collected from U.S. adults. Individuals are placed into a weight category based on weight, height, gender and age.

Underweight

Healthy Weight

Overweight (not Obese)

Obese

Probability

0.021

0.371

0.347

0.261

Based on this data, what is the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) range?

Your answer should be given to 3 decimal places.

Question 16

The probabilities for the amount that can be won on a lottery game are given in the table below. Find the missing probability X.

Amount($)

0

1

2

3

>3

Probability

0.53

0.27

X

0.04

0.01

X =

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