Question

A bag contains 5 black balls and 3 white balls. Two balls are drawn at random, one after another from the bag without replacement. What the probability that both of the balls have the same colour?

Answer 1

The answer depends on which color is picked two times.

Explanation:

Let's solve for black first. There is a `5/8` chance that a black marble will be chosen. A black marble is chosen without replacement. There are now 4 black marbles in a bag of 7 marbles, so there is a `4/7` chance that a black marble will be chosen. Let's now multiply the two fractions together to find our probability:

`(5/8)*(4/7)=20/56=5/14`

Let's now solve for white. There is a `3/8` chance that a white marble will be chosen. The marble is chosen and not replaced. There are now 2 white marbles in a bag of 7 marbles, so there is now a `2/7` chance that a white marble will be chosen. Let's multiply the two fractions together like last time:

`(3/8)*(2/7)=6/56=3/28`