Question

There are 2 red and 5 green balls in a bag. If you randomly choose balls one at a time , with replacement , What is the probability of choosing 2 green balls and then 1 red ball?

A. 2/21
B.20/147
C.50/343
D. 5/21

Answer 1

D is the answer

Explanation:

Answer 2

Option C

ANSWER:

The probability of choosing 2 green balls and 1 red ball is
`(50)/(343)`

SOLUTION:

Given, there are 2 red and 5 green balls in a bag.

So, there are 7 balls in the bag.

We need to find the probability of choosing 2 green balls and 1 red ball.

Probability of 2 green balls and 1 red ball = probability of 1st green ball
`*` probability of 2nd green ball x probability of 1 red ball.

Now, probability of 1st green ball =
`\frac{\text {number of green balls}}{\text {total number of balls}}`

=
`(5)/(7)`

because we are replacing after every pick.

Now, probability of red ball =
`\frac{\text {number of red balls}}{\text {total number of balls}}`

`=(2)/(7)`

Probability of 2 green balls and 1 red ball =
`(5)/(7) * (5)/(7) * (2)/(7)`

`=(5 * 5 * 2)/(7 * 7 * 7)`

`=(50)/(343)`

Hence, the probability of choosing 2 green balls and 1 red ball is
`(50)/(343)`