Q1: For safety reasons, 4 different alarm systems were installed in the vault co
ID: 3072945 • Letter: Q
Question
Q1: 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 0.88 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.
Q2: In a certain liberal arts college with about 10,000 students, 49% 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.
Q3: 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 41% 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 to two decimal places.
Q4: According to the information that comes with a certain prescription drug, when taking this drug, there is a 21% chance of experiencing nausea (N) and a 48% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% 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.
Q5: 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 51% 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.
Q6: An engineering school reports that 60% of its students are male (M), 32% of its students are between the ages of 18 and 20 (A), and that 20% 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.
Q7: An engineering school reports that 51% of its students were male (M), 33% of its students were between the ages of 18 and 20 (A), and that 27% 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.
Explanation / Answer
#1.
p = 0.88
P(X >= 1) = 1 - P(X=0)
= 1 - 0.88^0*(1-0.88)^4
= 0.9979
#2.
p = 0.49
Probability that both are of same gender 0.49^2 + 0.51^2 = 0.50020
#3.
P(only Nausea) = 0.15 - 0.1 = 0.05
#4.
P(N or D) = P(N) + P(D) - P(N and D)
= 0.21 + 0.48 - 0.15
= 0.54000
Required probability, P(N' and D') = 1 - P(N or D) = 0.46
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