Question

A bag contains five white balls and four black balls. Your goal is to draw two black balls.

You draw two balls at random. What is the probability that they are both black?

Answer 1

The probability that you draw two balls that are both black is
`(1)/(6)`

Explanation:

To find probability, take the number of desirable outcomes over the total number of possible outcomes.

In this case, the black balls are desirable. There are four of them.

this means the numerator of the first fraction is 4. The denominator is the total possible outcomes or in this case the total number of black and white balls. This number is 9. The first probability fraction is
`(4)/(9)`

Lets say that the first one was black. Now we need to find the probability of drawing another one. Now there are black balls left in the bag. This means that the number of desirable outcomes is 3. There are also 8 balls total. This means the number of total possible outcomes is 8. The second probability is
`(3)/(8)`

To get the total probability you multiply both of the individual probabilities together.

`(4)/(9) *(3)/(8) =(1)/(6)`