SOLUTION: the probability that person will pass A is 5/8 and the probability of person B will pass is 6/7. assume the events are independent. find the probability that at least one will pass

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Question 475135: the probability that person will pass A is 5/8 and the probability of person B will pass is 6/7. assume the events are independent. find the probability that at least one will pass
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to use the fact that P(At least one passing) = 1-P(Both Fail)




The probability that person will pass A is 5/8

So probability that person will NOT pass A is 1-5/8 = 3/8


The probability of person B will pass is 6/7


So probability of person B will NOT pass is 1-6/7 = 1/7

P(Both Fail) = P(A fails AND B fails)

P(Both Fail) = P(A fails) * P(B fails)

P(Both Fail) = (3/8)(1/7)

P(Both Fail) = 3/56

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So

P(At least one passing) = 1-P(Both Fail)

P(At least one passing) = 1-3/56

P(At least one passing) = 53/56