Question

Suppose you have a batch of 100 light bulbs, and 10% of them are defective. If you randomly select 15 light bulbs from the batch, with replacement, what is the probability that (a) exactly 2 of them are defective (b) at least two of them are defective

Answer 1

For 15 randomly selected light bulbs with replacement from a batch with a 10% defective rate, probabilities for exactly 2 or at least 2 defective bulbs can be calculated using the binomial probability formula or cumulative probability respectively.

Step-by-step explanation:

If you have a batch of 100 light bulbs, where 10% are defective, and you randomly select 15 light bulbs from the batch with replacement, the probability that:

1. Exactly 2 of them are defective can be calculated using the binomial probability formula, which is P(X=k) = nCk * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the binomial coefficient.
2. To find the probability of at least two defective light bulbs, you could calculate the probabilities for 0 and 1 defective light bulbs, then subtract these from 1 to get the cumulative probability for 2 or more defective bulbs.