Question 475135
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