Finite: Probability

Question

A jar has 8 Red, 11 White and 1 Blue marble. A marble is selected at random, its color noted and the marble is replaced. A second marble is selected from the 20 marbles

(a) What is the probability that both marbles selected were Red?

(b) What is the probability that exactly one of the marbles selected was Red?

(c) What is the probability that neither marble selected was Red?

(d) What is the probability that both marbles selected were the same color.

Answer 1

a) 8/20 = 2/5 on first draw. 7/19 on 2nd draw. 2/5 * 7/19 on both draws.

b) first one red = 8/20 and second one not red 12/19: probability of both = 8/20 * 12/19

first one not red = 12/20 and second one red 8/19: probability of both = 12/20 * 8/19

probability of either first one or second one red but both is sum of two probabilities

c) 12/20 not red on first draw; 11/19 not red on 2nd draw: 12/20 * 11/19 not red on both draws

d) probability both red - use probability from part a)

probability both white: 11/20 * 10/19

can't both be blue

sum probability same color is sum of first two probablities