Question

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are white

Answer 1

Out of 16 balls, two balls can be drawn in ¹⁶C₂ ways.
∴ Total number of elementary events = ¹⁶C₂ = 120

Out of seven white balls, two white balls can be chosen in ⁷C₂ ways.
∴ Favourable number of ways = ⁷C₂
Hence, required probability =

\[\frac{^{7}{}{C}_2}{^{16}{}{C}_2} = \frac{21}{120} = \frac{7}{40}\]