Four person independently solve a certain problem correctly with probabilities `1/2,3/4,1/4,1/8dot` Then the probability that he problem is solve corr

Question

Four person independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the probability that he problem is solve correctly by at least one of them is 235 256 b. 21 256 c. 3 256 d. 253 256 A. 235 256 B. 21 256 C. 3 256 D. 253 256 Select the correct answer from above options

Answer 1

Correct Answer - A PLAN It is simple application of independent event , to solve a certain problem or any type of compitition each event in independent of other . Formula used P(A∩B)=P(A)⋅P(B) , when A and B are independent events . Probability that the problem is solved correctly by atleast one of them =1- (problem is not solved by all ) ∴ P(problem is sovled ) =1- P(problem is not solved ) =1-P( ˉ A )⋅P( ˉ B )⋅P( ˉ C )⋅P( ˉ D ) =1-( 1 2 ⋅ 1 4 ⋅ 3 4 ⋅ 7 8 )=1- 21 256 = 235 256