a) Suppose that a female student being enrolled in engineering class drops the c

Question

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 class.

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.

Please give a brief explanation on how to set up these probability calulcations. In fact, provide me with the easiest how possible to remember how to set up the calculation.

Explanation / Answer

a) Given,

P(Drop rate) = 0.15

P(Male) = 0.80

P(Female) = 0.2

P(Drop|Female) = 0.1

By the formula:

P(Drop) = P(Drop|Male)*P(Male) + P(Drop|Female)*P(Female)

0.15 = P(Drop|Male)*0.80 + 0.1*0.20

So,

P(Drop|Male) = 0.13/0.80 = 0.1625

b) P(At least one fails) = 0.12

1 - P(No fails) = 0.12

P(No fails) = 1 - 0.12 = 0.88

Since both the components fail as well as not fail with the same probability. If we assume p as a probability of non failure. Then,

p2 = 0.88

p = 0.9381

So,

P(Both component fail) = (1 - 0.9381)2 = 0.0038 [Rounded off to 4 decimal places]

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