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Question:

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 45, then the probability that he is unable to solve less than two problems is

16425(15)48

545(45)48

2015(15)49

31625(45)48

Solution:

Correct option is B. 545(45)48
Given n=50, p=1/2
Let X be random variable which denotes number of problems that candidate is unable to solve
∴ p = 1/5 and X < 2 ⇒ P(X<2) = P(X=0) + P(X=1) = (4/5)^50 + 50C1 × (1/5) × (4/5)^49.