Question

There are a total of 15 balls in a bag.
The bag contains 3 balls of each of the following colours: red, green, blue, yellow and orange.
For $5.00, you can choose 3 balls (You cannot put the ball back after choosing it).

If you pick 3 balls and they all match in colour, you win the grand prize of 100 dollars. What is the probability of choosing 3 matching balls?

I did: (3C3 x 3C0 x 3C0 x 3C0 x 3C0/ 15C3) x 5C1
= (1/455) x 5C1
= 1/91

What did I do wrong?

Answer 1

Are you trying to find the probability of winning?

Answer 2

yes, of choosing 3 balls that match in color

Answer 3

So you have 5 colors.

You pick a ball.

It's a particular color.

There are 14 balls, left.

But only 2 of the 14 will result in a win.

You pick a ball on the second draw of the same color as the 1st with probability:

2/14

You pick a ball on the third draw of the same color as the 1st with probability

1/13

So the probability that the 2nd and 3rd draws are of the same color as the 1st is:

2/14 * 1/13 = 2/182=1/91

Answer 4

I get it, thank you!

Answer 5

you're welcome