Option C
ANSWER:
The probability of choosing 2 green balls and 1 red ball is [tex]\frac{50}{343}[/tex]
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 [tex]\times[/tex] probability of 2nd green ball x probability of 1 red ball.
Now, probability of 1st green ball = [tex]\frac{\text {number of green balls}}{\text {total number of balls}}[/tex]
= [tex]\frac{5}{7}[/tex]
because we are replacing after every pick.
Now, probability of red ball = [tex]\frac{\text {number of red balls}}{\text {total number of balls}}[/tex]
[tex]=\frac{2}{7}[/tex]
Probability of 2 green balls and 1 red ball = [tex]\frac{5}{7} \times \frac{5}{7} \times \frac{2}{7}[/tex]
[tex]=\frac{5 \times 5 \times 2}{7 \times 7 \times 7}[/tex]
[tex]=\frac{50}{343}[/tex]
Hence, the probability of choosing 2 green balls and 1 red ball is [tex]\frac{50}{343}[/tex]
