Question

Question 1)

For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 4 systems detects theft with a probability of 0.82 independently of the others.

The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 4 systems will detect it. What is the probability that when a theft occurs, at least one of the 4 systems 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 certain prescription drug, when taking this drug, there is a 15% chance of experiencing nausea (N) and a 46% 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 neither of the side effects?

Your answer should be to two decimal places.

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Question 3

According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% 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 nausea or a decrease in sexual 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), and that 34% 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.

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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 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.

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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 or between the ages of 18 and 20?

Your answer should be rounded to two decimal places.

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Question 7

Let A and B be two independent events such that P(A) = 0.14 and P(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 and P(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 and P(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 and P(B) = 0.54.

What is P(A or B)

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Question 11

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 0.377 0.359 0.243

Based on this data, what is the probability that a randomly selected 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 lottery game are given in the table below. Find the missing probability X.

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

X =

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Answer 1

Answer 1: The system detects theft with a probability of 0.82.

Therefore, the system does not detect theft with a probability of 1-0.82=0.18

The complement of​ "at least​ one" is​ "none." So, the probability of getting at least one detect theft is equal to 1-​P(none detect theft).

Therefore, the probability that when a theft occurs, at least one of the 4 systems will detect it is:

P(at least one detect theft) = 1 - ​P(none detect theft)

                                          = 1 - 0.18⁴

                                          = 1 - 0.00105

                                          = 0.99895

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Answer 2: Given P(N) = 0.15, P(D) = 0.46 and P(N and D) = 0.10

The probability of experiencing either of the side effects is:

P(N or D) = P(N) + P(D) - P(N and D)

                = 0.15 + 0.46 - 0.10

                = 0.51

The probability of experiencing neither of the side effects is:

P(N or D)^c = 1 - P(N or D)

                = 1 - 0.51

                = 0.49

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Answer 3: Given P(N) = 0.18, P(D) = 0.50 and P(N and D) = 0.11

The probability of experiencing nausea or a decrease in sexual drive is:

P(N or D) = P(N) + P(D) - P(N and D)

                = 0.18 + 0.50 - 0.11

                = 0.57

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Answer 4: Given P(M) = 0.55, P(A) = 0.39 and P(M and A) = 0.34

The probability of a random student being chosen who is a male or is between the ages of 18 and 20 is:

P(M or A) = P(M) + P(A) - P(M and A)

                = 0.55 + 0.39 - 0.34

                = 0.60

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

P(F and A^C) = P(M or A)^c = 1 - P(M or A)

                    = 1 - 0.60

                    = 0.40