Suppose that a shop has an equal number of LED bulbs of two different types.…
2024
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.
0.44
- B.
0.55
- C.
0.66
- D.
0.77
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Correct Option
Option B: 0.55
Summary Solution
The Law of Total Probability is applied by multiplying the prior probability of each bulb type (0.5) by their respective probabilities of lasting more than 100 hours (0.7 and 0.4) and summing the results.
Since the shop has an equal number of LED bulbs, the prior probability for each type is 0.5. Applying the Law of Total Probability: P(Last > 100) = (0.5 * 0.7) + (0.5 * 0.4) = 0.35 + 0.20 = 0.55.