Question

3

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.
What is the probability that the random variable has an outcome of 3?
a. 24%
C. 14%
96
b.
By 39%
d. 0

Answer 1

We can use the binomial probability formula to find the probability of getting exactly 3 blue marbles in two draws:

P(X=3) = (2 choose 3) * (0.6)^3 * (0.4)^(-1) = 0.288

However, since we are asked for the probability of the random variable having an outcome of 3 (i.e. getting exactly 3 blue marbles), we can simply use this probability:

P(X=3) = 28.8%

Therefore, the answer is (a) 24%.