Question

A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. 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. What is the probability that the random variable has an outcome of 3?

Answer 1

5/8

Explanation:

Find P(x = 3 blues for the 2 draws)

two draws

Binomial probability.

we know p = 3/8 for blue, else q = 1 - q = 1 - (3/8)

X = # of blue marbles left in the bag.

apparently it looks like there are 8 marbles in the bag, 3 are blue, 5 are red

X = 3 , means the draw was a red 5/8 for the first draw

the 2nd draw can be a blue or a red so, probability is 1

P(X = 3) = (5/8) * 1 = 5/8

Answer 2

D. 0 is the answer took the test and got it right