Question

A bag of marbles has 4 green, 6 blue and 9 red. If 4 marbles are drawn out of the bag without looking, what is the probability that there will be 3 red marbles and 1 blue marble?

Answer 1

`42/323`

Explanation:

You could draw a tree diagram but quite fiddly with four selections. You could pick:
R R R B
R R B R
R B R R
B R R R
The order they are picked does not matter but you have to include all four different ways in your answer

Line one would be :
`9/19` x `8/18` x `7/17` x `6/16` = `21/646`
Line two would be:
`9/19` X `8/18` X `6/17` X `7/16` = `21/646`
This continues so that you have `21/646` four times. When you add them together it equals `42/323`

The denominator goes down from 19 to 18 to 17 to 16 because the number of marbles decreases by one each time you remove one from the bag.
The numerator goes from 9 to 8 to 7 because there are 9 red marbles then 8 and then 7. There are 6 blue marbles so that is why the numerator 6 is used.
You add all four answers together because al four of the ways of selecting the marbles add to your answer.