A box of 10 flashbulbs contains defective . A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in the sample. a. Find the probability distribution of X. b. Find the expected number of defective bulbs in a sample.

(a)

(b)

Step-by-step explanation:

Given

--- flashbulbs

--- defective bulbs

--- selected

Solving (a): The distribution of x

The total outcome is:

This gives:

Having 3 defective bulbs means 7 are not.

When there is no defective bulb among the selected, the probability is:

When 1 is defective:

When both are defective

So, the distribution is:

Solving (b): The expected value

This is calculated as:

So, we have:

The equation becomes:

From the distribution in (a), we have:

Simplify