A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. Two marbles are picked at random. What is the fractional probability that 2 red marbles are picked if the first marble was returned before the second was chosen?

Answer 1

First, we need to calculate the total number of ways to select 2 marbles out of 12:

Total outcomes = (4 + 5 + 3) choose 2 = 12 choose 2 = 66

Next, we need to calculate the number of ways to select 2 red marbles out of the 4 available:

Number of ways to select 2 red marbles = 4 choose 2 = 6

Therefore, the probability of selecting 2 red marbles is:

Probability = Number of ways to select 2 red marbles / Total outcomes = 6 / 66 = 3 / 33 = 1 / 11

So the fractional probability that 2 red marbles are picked if the first marble was returned before the second was chosen is 1/11.