Help Please!!! .

Question

A bag contains 9 marbles: 3 are green, 2 are red, and 4 are blue. Linda chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.

Answer 1

For the first selection since there are 4 blue marbles, the probability of choosing a blue marble is 4/9.

After the first selection, there are 3 blue marbles and 8 marbles total, so the probability of choosing a blue marble on the second draw is 3/8.

The probability of choosing a blue marble in both draws is thus 4/9 * 3/8= 12/72 = 1/6

In formula terminology:

event A = choose marble on 1st draw

event B = choose marble on 2nd draw

P(A and B) = P(B|A)/P(A), where P(B|A) is probability event B occurring given event A has occurred.

P(A) = 4/9

P(B|A) = 3/8

P(A and B) = 4/9 * 3/8 = 1/6