SOLUTION: A missile can be accidentally launched if two relays A and B both have failed. the probabilities of A and B failing known to be 0.01 and 0.03 respectively. It is also known that B

Question 328423: A missile can be accidentally launched if two relays A and B both have failed. the probabilities of A and B failing known to be 0.01 and 0.03 respectively. It is also known that B is more likely to fail(probability 0.06) if A has failed.
a)What is the probability of an accidental missile launch?
b)What is the probability that A will fail if B has failed?
c)Are the events "A fails" and "B fails" statistically independent?
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
Probability B fails given A fails, P(B|A), is given as .06
P(A)=.01
P(B)=.03
part a would be the probability A and B fail, P(A and B)
P(B|A)=P(A and B)/P(A)
.06=P(A and B)/.01
P(A and B)=.0006
part b, P(A|B)=P(A and B)/P(B)
We now have P(A and B)=.0006 from part a. Use this to answer part b.
P(A|B)=.0006/.03=.02
part c, the events are independent if the occurence of one does not affect the occurence of the other. That is, if P(B|A)=P(B) or P(A|B)=P(A) they are independent.
Are they the same?.
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