15. Suppose that 60% of drivers are \"careful\" and 40% are \"reckless.\" Suppos
ID: 3321251 • Letter: 1
Question
15. Suppose that 60% of drivers are "careful" and 40% are "reckless." Suppose further that a careful driver has a 0.1 probability of being in an accident in a given year, while for a reckless driver the probability is 0.4. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)
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16. Use the given values to find the following. (Enter your answers as fractions.)
P(A) = 0.5, P(B) = 0.5, P(A B) = 0.1
(a) P(A given B)
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(b) P(B given A)
2
17. A box contains 5 white, 2 red, and 5 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)
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18. Two students are registered for the same class and attend independently of each other, student A 70% of the time and student B 60% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.)
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19. Two students are registered for the same class and attend independently of each other, student A 70% of the time and student B 60% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.)
Explanation / Answer
Answers
As per chegg policy, if there are more than one question, experts are required to provide answer to the first question only. Here I am providing answers to first 2 questions.
15. Let C and R respectively be the events that the drivers are careful and reckless. Let A be the event that the driver being in an accident in a given year.
Given that P (C) = 0.6, P (R) = 0.4, P (A|C) = 0.1, P (A|R) = 0.4
We need P (A)
P (A) = P (C) * P (A|C) + P (R) * P (A|R)
= (0.6 * 0.1) + (0.4 * 0.4) = 0.06 + 0.16 = 0.22
16.
a. P (A|B) = P(A B)/P (B) = 0.1/0.5 = 1/5
b. P (B|A) = P(A B)/P (A) = 0.1/0.5 = 1/5
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