Question

A bag contains 7 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be red?

Answer 1

5.1%

Explanation:

A bag contains 7 red marbles, 6 blue marbles and 4 green marbles, 17 marbles in total.

Number of red marbles = 7

Number of all marbles = 17

Number of choices 3 red marbles out of 7 red marbles
`=C^7_3=(7!)/(3!(7-3)!)=(7!)/(3!\cdot 4!)=35`

Number of choices 3 marbles out of 17 marbles
`=C^(17)_3=(17!)/(3!(17-3)!)=(17!)/(3!\cdot 14!)=17\cdot 8\cdot 5=680`

The probability that all three marbles drawn will be red is

`(35)/(680)=(7)/(136)\approx 0.0514705\approx 5.1\%`