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

Option C

ANSWER:  

The probability of choosing 2 green balls and 1 red ball is

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 =

=

because we are replacing after every pick.

Now, probability of red ball =

Probability of 2 green balls and 1 red ball =

Hence, the probability of choosing 2 green balls and 1 red ball is

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square