Question

There are 3 different brands of fluorescent bulbs in a box. The probability that a A...

There are 3 different brands of fluorescent bulbs in a box. The probability that a A brand bulb will last for over 100 hours is 0.7; the probability that a B brand bulb will last for over 100 hours is 0.4 and the probability that a C brand bulb will last for over 100 hours is 0.3. Suppose that 20% of the bulb in that box are A brand, 30% are B brand, and 50% are C brand. And the bulb is picked at random.

a. What is the probability that a bulb will last for over 100 hours?

b. Given that the bulb lasted for over 100 hours, what is the probability that it is from A brand?

Math   Statistics-And-Probability   
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Answer #1

(a) P(Bulb lasts for over 100 hours)

Probability of picking a bulb of Brand A and that it will last for over 100 hours = 0.2 * 0.7 = 0.14

Probability of picking a bulb of Brand B and that it will last for over 100 hours = 0.3 * 0.4 = 0.12

Probability of picking a bulb of Brand C and that it will last for over 100 hours = 0.5 * 0.3 = 0.15

Therefore the required probability = 0.14 + 0.12 + 0.15 = 0.41

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(b) P(Bulb is Brand A given it last for over 100 hours)

By Bayes Theorem, P(A/B) = P(A and B)/P(B)

Therefore, P(Bulb is Brand A given it last for over 100 hrs) = P(Brand A and lasts for over 100 hrs)/P(Bulb lasts for 100 hours)

= 0.14/0.41

= 0.3415

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