Suppose that a very large box that contains cameras and that 3/7 of them are defective. A sample of 2 cameras is selected at random.

Question

Suppose that a very large box that contains cameras and that 3/7 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample.

1. Write the probability distribution for X. Round to two decimal places. 

X	P(X)

1. What is the expected value of X? Round to two decimal places.

Answer 1

If box large, we can consider each sample independent

Probability getting 0 is 4/7 * 4/7 = 16/49

Probability getting 1 is 3/7 * 4/7 * 2 (can either be 1st or 2nd is defective) = 24/49

Probability getting 2 is 3/7 * 3/7 = 9/49