Question

A bag contains 5 red marbles, 4 blue marbles and 7 green marbles. If three marbles

are drawn out of the bag, what is the exact probability that all three marbles drawn
will be red?

Answer 1

The exact probability that all three marbles drawn will be red is
`(1)/(56)`

Explanation:

Number of red marbles = 5

Number of blue marbles = 4

Number of Green marbles = 7

Total Number of marbles = 5+4+7=16

We are given that three marbles are drawn out of the bag

Probability of getting 1 red marble on first draw=
`(5)/(16)`

Probability of getting 1 red marble on second draw=
`(4)/(15)`

Probability of getting 1 red marble on third draw=
`(3)/(14)`

So,the exact probability that all three marbles drawn will be red=
`(5)/(16) * (4)/(15) * (3)/(14)=(1)/(56)`

Hence The exact probability that all three marbles drawn will be red is
`(1)/(56)`