Question

You randomly select 2 marbles from a mug containing 6 blue marbles, 6 red marbles, and 3 white marbles. How many times greater is the probability of selecting 2 red marbles when you replace the first marble before selecting the second marble than when you do not replace the first marble before selecting the second marble?

Answer 1

Given: n(S) = 15, n(B) = n(R) = 6 and n(W) = 3

Probability of selecting 2 red marbles, with replacement: Once we select the first red ball from 6 of them, we replace the red ball into the mug. Hence, during the 2nd draw we would still be drawing a red ball from 6 of them. The total no. of balls ( n = 15) would also remain the same in both draws.

= 0.160

Probability of selecting 2 red marbles, without replacement: Once we select the first red ball from 6 of them, we do not replace the red ball into the mug. Hence, during the 2nd draw we would be drawing a red ball from 6 - 1 = 5 of them. The total no. of balls ( n = 15) would also reduce to 15 - 1 = 14 balls in the 2nd draw.

= 0.143

Hence, the probability of selecting 2 red marbles when we replace the first marble before selecting the second marble is:

0.160 / 0.143 = 1.119

1.119 times greater than when we do not replace the first marble before selecting the second marble.