Suppose that a shop has an equal number of LED bulbs of two different types.…
2016
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 ____________ .
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Correct answer: 0.55
Use the law of total probability because the shop has equal numbers of the two types.
Probability a randomly chosen bulb is Type 1 = 1/2. Contribution to lasting more than 100 hours = 1/2 × 0.7 = 0.35.
Probability a randomly chosen bulb is Type 2 = 1/2. Contribution to lasting more than 100 hours = 1/2 × 0.4 = 0.20.
Add the contributions: 0.35 + 0.20 = 0.55.
Therefore, the probability that a randomly chosen bulb lasts more than 100 hours is 0.55.