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Question:

Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then the probability that the problem is solved correctly by at least one of them is?

235/256

32/56

253/256

212/56

Solution:

P(A)=1/2 ⇒P(¬A)=1/2
P(B)=3/4 ⇒P(¬B)=1/4
P(C)=1/4 ⇒P(¬C)=3/4
P(D)=1/8 ⇒P(¬D)=7/8
P(at least one of them solves correctly)=1−P(none of them solves correctly)=1−(1/2 × 1/4 × 3/4 × 7/8)=235/256