Finite Math: Probability

Question

A container has 7 red marbles, 3 white marbles, and 5 blue marbles. A marble is selected at random from these 15 marbles, its color is noted and it is replaced. A second marble is selected from the 15 and its color is noted.

(a) What is the probability that neither marble selected is red?

(b) What is the probability that both marbles selected are the same color?

(c) What is the probability that exactly one of the marbles selected is red?

Answer 1

a) So we have sampling with replacement: So every scenario will be 15 marbles with the same proportion.

1. We have 7 red marbles, so the amount that are not red marbles are 8.
2. So we have a probability of 8/15. Since these events are independent we just multiply them twice. (8/15)^2=(8/15)*(8/15)

b) Both are the same color, take the same approach. You already have the red part form part a.

1. P(both red)+P(both white)+P(both blue)

c) Find all the scenarios where you have one red.

Hint: 1- P(no red)-P(both red)