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 (rounded off to 1 decimal place) that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.

GATE 2016 · Engineering Mathematics · Conditional Probability · medium

Answer: 0.55

1. State the Law of Total Probability: P(T1) = 0.5, P(T2) = 0.5, P(L|T1) = 0.7, P(L|T2) = 0.4.
2. Substitute and compute: P(L) = 0.35 + 0.20 = 0.55.