Problem 1 (25 points) a) Suppose that a female student being enrolled in enginee

Question

Problem 1 (25 points) a) Suppose that a female student being enrolled in engineering class drops the class with probability 0.1, while the overall drop rate is 0.15. It is known that 80 percent of the students in engineering programs are male. Compute the probability that a male student drops an engineering clas b) A car is equipped with a dual brake system relying on two components C1 and C2. The probability that at least one of the components fails within a one-year period is 0.12 Assuming that each component fails with the same probability, and that failure of C1 and C2 are independent events, compute the probability that both components fail.

Explanation / Answer

a) P(drop|female)= 0.1, P(drop)= 0.15, P(male)=0.8 ,thus P(female and drop)=P(drop|female)*P(female)= 0.1*0.2=0.02

P(male and drop)=0.15-0.02=0.13, thus P(drop|male)=P(male and drop)/P(male) =0.13/0.8=0.1625

b) A: C1 fails , B: C2 fails

P(A or B)=0.12, P(A)=P(B)=x, since the events are independent P(A and B)=P(A)*P(B)=x^2

Thus P(A or B)=P(A)+P(B)-P(A and B)=0.12=2x-x^2

12=200x-100x^2

100x^2-200x+12=0

x=0.061

Thus P(A and B)=x^2=(0.061)^2 =0.003721

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