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1 votes
1 votes
A computer program selects an integer in the set {k : 1 ≤ k ≤ 10,00,000} at random and prints out the result. This process is repeated 1 million times. What is the probability that the value k = 1 appears in the printout atleast once ?

(A) 0.5 (B) 0.704 (C) 0.632121 (D) 0.68

1 Answer

4 votes
4 votes
Let n=10,00,000 (1 million)

Probability that the value k=1 appears at least once= nC1 (1/1 million)* (1-1/1million)^(n-1) + nC2 (1/1 million)^2 *(1- 1/1 million)^(n-2) +..................

which can be simplified to     1 - nC0 (1 - 1/ 1million)^n

 OR

Probability=1- (No. of times 1 doesn't appear/Total no. of times process is repeated)^Total no. of times process is repeated

=1 - (999999/1000000)^1000000

=0.632121

This fraction might seem too tedious to calculate so you may just shorten the question like finding out probability if process is repeated 1000 times. then also the probability comes out nearly 0.632.

Moreover, you may just look at the options and eliminate the options.

Hence, C is the answer.
edited by

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