GATE CS 2016 Set 2 — Question 15
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Engineering Mathematics → Probability & Statistics → Conditional Probability
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Question
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 _________.
Correct answer
0.55 to 0.55
Solution
Let be the event that the bulb lasts more than 100 hours.
Let be the event that the bulb is of Type 1.
Let be the event that the bulb is of Type 2.Given:
(equal number of bulbs)
Using the Law of Total Probability:The probability is 0.55.
Let be the event that the bulb is of Type 1.
Let be the event that the bulb is of Type 2.Given:
(equal number of bulbs)
Using the Law of Total Probability:The probability is 0.55.
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