Question 467827: I need a tutor to show me if I did these problems the correct way.
1. Given Pr(E) = 0.6, Pr(F) = 0.4, and Pr(E∩F) = 0.3. Find Pr(E|F).
0.3/0.4= 0.75
2. Suppose A, B, and C are three independent parts in a machine. The probability of failing in its first 1000 hours of use is 0.1 for A, 0.2 for B, and 0.4 for C. Find the probability that all three parts function WITHOUT failure in their first 1000 hours of use.
0.1 x 0.2 x 0.4= .008 = 1/125
3. Suppose E and F are independent events. If Pr(E) = 0.4, Pr(F) = 0.7, then Pr(EUF) = ____.
0.4 x 0.7= .28
1.1 -.28= .82
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! 1. Correct.
2. A, B, and C being three independent events ==> A', B', C' (their complements) are also independent.
==> The probability that all three parts function WITHOUT failure in their first 1000 hours of use is 0.9*0.8*0.6 = 0.432.
3. P(E U F) = P(E) + P(F) - P(E)*P(F) = 0.4 + 0.7 - 0.28 = 0.82.
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