Two balls are drawn at random from the bag. What will be the probability that both the balls are red?
$\dfrac{8}{95}$
$\dfrac{9}{95}$
$\dfrac{9}{10}$
$\dfrac{18}{95}$
$\dfrac{5}{19}$
Solution
Total possible outcomes
= Selection of 2 balls out of (9 + 7 + 4 =) 20 balls
$= ^{20}C_2 = \dfrac{20 \times 19}{ 1 \times 2}$ = 190
Favourable outcomes = Selection of 2 balls out of 9 red balls
$= {^9}C_2 = \dfrac{9 \times 8}{1 \times 2} = 36$
$\therefore$ Required probability
$= \dfrac{36}{190} = \dfrac{18}{95}$