Correct Answer - Option 1 : 4/15
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement.
Let P1(E) denotes the probability that the first ball drawn is red.
Let P2(E) denotes the probability that the second ball drawn is green.
As there are total 16 balls and we need to select one red ball
There are 8 red balls.
\({P_1}\left( E \right) = \frac{{{8_{{c_1}}}}}{{16{c_1}}} = \frac{8}{{16}} = \frac{1}{2}\)
Now the total balls will become 15 and the number of green balls is 8.
We need to select a ball from 8 green balls.
\({P_2}\left( E \right) = \frac{{{8_{{c_1}}}}}{{16{c_1}}} = \frac{8}{{15}}\)
As P1(E) and P2(E) both are independent
P(E) = P1(E). P2(E)
\(= \frac{1}{2} \times \frac{8}{{15}} = \frac{4}{{15}}\)