# GATE | GATE-CS-2016 (Set 2) | Question 15

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is :

(A) 0.55
(B) 0.7
(C) 0.4
(D) 0.35

Explanation: The question is based on Bayes’ Theorem.

P(LED is Type 1) = 1/2
P(LED is type 2) = 1/2

Now, we need to see conditional probabilities.

P( LED lasting more than 100 hours / LED is Type 1) = 0.7
P( LED lasting more than 100 hours / LED is Type 2) = 0.4

P(LED lasts more than 100 hours) = P( LED is Type1)* P(LED lasting more than 100 hours / LED is Type 1) + P(LED is Type 2) * P( lasting more than 100 hours / Type 2)

= 0.5 * 0.7 + 0.5 * 0.4
= 0.35 + 0.20
= 0.55

Thus, A is the correct choice.

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