Question

In a certain shipment of 11 modems, 5 are defective. 6 of the modems are selected at random without replacement. What is the probability that 3 of the 6 modems are defective?

Answer 1

To find the probability that 3 of the 6 modems are defective, we need to use the hypergeometric distribution. The probability is 0.5.

Step-by-step explanation:

To find the probability that 3 of the 6 modems are defective, we need to use the hypergeometric distribution. Here's how:

1. Define the random variable X as the number of defective modems chosen.
2. Calculate the number of ways to choose 3 defective modems out of 5: C(5, 3) = 10.
3. Calculate the number of ways to choose 3 modems out of the total 6: C(6, 3) = 20.
4. The probability that 3 of the 6 modems are defective is 10/20 = 0.5.