​A box contains 2 black, 6 green and 4 yellow balls. If 2 balls are picked up at random, the probability that both are green-coloured is: ​

Correct option is A

Given:

Total number of balls = 2 black + 6 green + 4 yellow = 12 balls

Green balls = 6

Number of balls picked = 2

Formula Used:

Probability  $$= \frac{k}{n} \times \frac{k-1}{n-1}$$

​n is the total number of objects

​k is the number of objects of the specific type

Solution:

P(both green) = $$\frac{\text{Number of ways to pick 2 green balls}}{\text{Total number of ways to pick 2 balls}}$$​​

Total number of ways to pick 2 balls from 12:

= $$\frac{12\times 11} {2}$$ = 66

Number of ways to pick 2 green balls from 6:

=$$\frac{6\times 5} {2}$$=15

Probability:

$$P(\text{both green}) =$$$$\frac{15}{66}= \frac{5}{22}$$

Thus, option (A) is right.