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 :-

(a) 235/256

(b) 21/256

(c) 3/256

(d) 253/256


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Answer 1

Answer:

Step-by-step explanation:

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Correct answer is

Option A

Answer 2

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 :-

Let P(A) be 1/2,

P(B) be 3/4,

P(C) be 1/4,

P(D) be 1/8.

Probability that A is wrong = 1 - 1/2

= 1/2.

Probability that B is wrong = 1 - 3/4

= 1/4.

Probability that C is wrong = 1 - 1/4

= 3/4.

Probability that D is wrong = 1-1/8

= 7/8.

Probability that none of them solve it = 1/2 * 1/4 * 3/4 * 7/8

= 21/256

Then the probability that the problem is solved correctly by at least one of them is = 1 - 21/256

(complimentary)

= 235/256.