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UGC-NET | UGC NET CS 2014 Dec – II | Question 4
• Last Updated : 26 Jun, 2018

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

Answer: (C)

Explanation: Favorable outcome k = 1
Total outcome = 1000000 = 106
Probability of k = 1;
Probability = favorable outcome / total outcome
= 1 / 106 = 10-6
Probability of k != 1:
= 1 – Probability of k = 1;
1 – 10-6 = 0.999
Probability that k = 1 is never printed in all 106 printouts:
= 0.999*0.999*…….0.9999 (106 time)
= 0.999106
Probability that 1 is printed at least once:
= 1- probability that 1 is never printed
= 1-0.99910^6
=0.6321
So, option (C) is correct.

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