UGC NET CS 2018 July - II Question 84

Question 84

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84. Digital data received from a sensor can fill up 0 to 32 buffers. Let the sample space be S={0, 1, 2, .........., 32} where the sample j denote that j of the buffers are full and
p(i) = (1 / 561) (33 - i). Let A denote the event that the even number of buffers are full. Then p(A) is :

Options:

1. (1) 0.515
2. (2) 0.785
3. (3) 0.758
4. (4) 0.485

Answer : (1) 0.515

Explanation Question 84

Probability of i th buffer getting full = p(i) = 1 / 562 (33 − i)
Probability of all even number of buffers are full is P(A)

P(A) = Σ _{i = 0, 2, 4, .., 32} P(i) = Σ _{i = 0, 1, 2, .., 16} P(2i)

We are going find the values of P(0), P(2), P(4), P(6) .... P(16).
P(0) = 1 / 562 (33 - 0)
P(2) = 1 / 562 (33 - 2)
...
P(16) = 1 / 562 (33 - 32)

The probability of all even number of buffers are full is P(A) which is equal to
P(0) + P(2) + P(4) + P(6) + .... P(16).
P(A) = 1 / 562(33 + 31 + 29 + 27 + .... + 1)
P(A) =(1 / 562) * 289
= 0.51423 = 0.515

So, Option (1) is correct answer.

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