Question 1)

For safety reasons, 4 different alarm systems were installed inthe vault containing the safety deposit boxes at a Beverly Hillsbank. Each of the 4 systems detects theft with a probability of0.82 independently of the others.

The bank, obviously, is interested in the probability that whena theft occurs, at least one of the 4 systems will detect it. Whatis the probability that when a theft occurs, at least one of the 4systems will detect it?

Your answer should be rounded to 5 decimal places.

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Question 2

According to the information that comes with a certainprescription drug, when taking this drug, there is a 15% chance ofexperiencing nausea (N) and a 46% chance of experiencing decreasedsexual drive (D). The information also states that there is a 10%chance of experiencing both side effects.

What is the probability of experiencing neither of the sideeffects?

Your answer should be to two decimal places.

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Question 3

According to the information that comes with a certainprescription drug, when taking this drug, there is a 18% chance ofexperiencing nausea (N) and a 50% chance of experiencing decreasedsexual 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 insexual drive?

Your answer should be rounded to 2 decimal places.

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Question 4

An engineering school reports that 55% of its students are male(M), 39% of its students are between the ages of 18 and 20 (A), andthat 34% are both male and between the ages of 18 and 20.

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

Your answer should be to two decimal places.

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Question 5

An engineering school reports that 53% of its students were male(M), 36% of its students were between the ages of 18 and 20 (A),and that 28% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is afemale or between the ages of 18 and 20? Assume P(F) = P(notM).

Your answer should be given to two decimal places.

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Question 6

An engineering school reports that 54% of its students were male(M), 39% of its students were between the ages of 18 and 20 (A),and that 25% were both male and between the ages of 18 and 20.

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

Your answer should be rounded to two decimalplaces.

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Question 7

Let A and B be two independent events such that P(A) = 0.14 andP(B) = 0.76.

What is P(A or B)?

Your answer should be given to 4 decimal places.

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Question 8

Let A and B be two independent events such that P(A) = 0.3 andP(B) = 0.6.

What is P(A and B)?

Your answer should be given to 2 decimal places.

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Question 9

Let A and B be two disjoint events such that P(A) = 0.24 andP(B) = 0.33.

What is P(A and B)?

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Question 10

Let A and B be two disjoint events such that P(A) = 0.08 andP(B) = 0.54.

What is P(A or B)

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Question 11

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

Underweight Healthy Weight Overweight (not Obese) Obese Probability 0.021 0.377 0.359 0.243

Based on this data, what is the probability that a randomlyselected U.S. adult weighs more than the healthy weight range?

Your answer should be given to 3 decimal places.

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Question 12

The probabilities for the amount that can be won on a lotterygame are given in the table below. Find the missing probabilityX.

Amount($) 0 1 2 3 >3 Probability 0.52 0.27 X 0.04 0.01

X =

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