Probability 5 Question 1

1. 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 problem is

(2019 Main, 12 April II)

(a) 201515

(b) 3162545

(c) 54545

(d) 164251548

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Answer:

Correct Answer: 1. (c)

Solution:

  1. Given that, there are 50 problems to solve in an admission test and probability that the candidate can solve any problem is 45=q (say). So, probability that the candidate cannot solve a problem is p=1q=145=15.

Now, let X be a random variable which denotes the number of problems that the candidate is unable to solve. Then, X follows binomial distribution with parameters n=50 and p=15.

Now, according to binomial probability distribution concept

P(X=r)=50Cr15r4550r,r=0,1,,50

Required probability

=P(X<2)=P(X=0)+P(X=1)=50C04550+50C1449(5)50=454945+505=5454549



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