Question

The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is

• A. 0.9
• B. 0.01
• C. 0.119
• D. 0.891

Hint:

When dealing with conditional probabilities, always ensure that the total probability theorem is used for scenarios with multiple possible outcomes.

Answer 1

The Correct Option is D

Let \(P(F)\) be the event that the electronic component fails when first used. So, \[ P(F) = 0.10 \quad {and} \quad P(F') = 1 - P(F) = 0.90 \] Let \(E\) be the event that a new component will last for one year, then \[ P(E) = P(F) \cdot P(E | F) + P(F') \cdot P(E | F') \] Using the total probability theorem, we have: \[ P(E) = 0.10 \times 0 + 0.90 \times 0.99 = 0.891 \] Thus, the probability that the new component will last for one year is \(0.891\).