Question

A bag contains red and blue marbles, such that the probability of drawing a blue marble is an experiment consists of drawing

a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of
blue marbles to each outcome.
Calculate the expected value of the random variable

Answer 1

3/4

Explanation:

I assume the probability of selecting a blue marble is 3/8.

The probability of selecting 0 blue marbles is:

P = (5/8) (5/8) = 25/64

The probability of selecting 1 blue marble is:

P = (3/8) (5/8) + (5/8) (3/8) = 30/64

The probability of selecting 2 blue marbles is:

P = (3/8) (3/8) = 9/64

So the expected value is:

E(X) = (0) (25/64) + (1) (30/64) + (2) (9/64)

E(X) = 3/4