Question

A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.

Find the probability that the second gumball is red.

Answer 1

Answer: 4/9

===================================================

Work Shown:

5 blue + 4 red = 9 total

A = P(1st is red, 2nd is red)

A = P(1st is red)*P(2nd is red, given 1st is red)

A = (4/9)*(3/8)

A = 12/72

B = P(1st is blue, 2nd is red)

B = P(1st is blue)*P(2nd is red, given 1st is blue)

B = (5/9)*(4/8)

B = 20/72

C = P(2nd is red)

C = A+B

C = 12/72 + 20/72

C = 32/72

C = 4/9