Based on these percentages, approximate the probability that a given power failu

Question

Based on these percentages, approximate the probability that a given power failure involves (a) line damage given that there is transformer damage (b) transformer damage given that there is line damage (c) transformer damage but not line damage (d) transformer damage given that there is no line damage (e) transformer damage or line damage Let A_1 and A_2 be events such that P[A_1] = 5, P[A_2] = 7. What must P[A_1 intersection A_2] equal for A_1 and A_2 to be independent? Let A_1 and A_2 be events such that P[A_1] = 6, P[A_2] = 4, and P[A_1 union A_2] = 8. Are A_1 and A_2 independent? Consider your answer to Exercise 14(b). Are the events A_1: the backup engine functions, and A_2: the main engine fails independent? Studies in population genetics indicate that 39% of the available genes for determining the Rh blood factor are negative. Rh negative blood occurs if and only if the individual has two negative genes. One gene is inherited independently from each parent. What is the probability that a randomly selected individual will have Rh negative blood?

Explanation / Answer

two events A and B are independent if P(A and B) = P(A) . P(B)

=>

P(A1 and A2) = P(A1) * P(A2)

= 0.5 * 0.7

= 0.35

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