An urn contains 6 red, 4 blue, 2 green 3 yellow marbles. If two marbles are drawn at random from the run, what is the probability that both are red ?

Solution (By Examveda Team)

Total number of balls = (6 + 4 + 2 + 3) = 15
Let E be the event of drawing 2 red balls.
Then, n(E)  $$ = {}^6\mathop C\nolimits_2 $$  $$ = \frac{{6 \times 5}}{{2 \times 1}}$$   = 15
Also, $$n(S) = {}^{15}\mathop C\nolimits_2 $$   $$ = \frac{{15 \times 14}}{{2 \times 1}}$$   = 105
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{15}}{{105}} = \frac{1}{7}$$