Question

A box contains 6 red and 8 green marbles. You reach in and remove 3 marbles all at once.

(a) Find the probability that these 3 marbles are all red. (Enter your answer as a fraction.)


(b) Find the probability that these 3 marbles are all of the same color. (Enter your answer as a fraction.)

Answer 1

Answer:
`(5)/(91),(38)/(182)`

Explanation:

(a)Probability that these three marbles are all red

choosing 3 red out of 6 is given by
`^6C_3`

and choosing 3 marble from 14 marbles=
`^(14)C_3`

`Probability=(^6C_3)/(^(14)C_3)=(5)/(91)`

(b)All of same color

It is possible when they are of either red or green

For red it is
`(^6C_3)/(^(14)C_3)`

For Green it is

`(^8C_3)/(^(14)C_3)`

total=
`(^6C_3)/(^(14)C_3)+(^6C_3)/(^(14)C_3)`

=
`(38)/(182)`