# An Urn Contains 7 White, 5 Black and 3 Red Balls. Two Balls Are Drawn at Random. Find the Probability that One Ball is White. - Mathematics

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that  one ball is white.

#### Solution

Out of 15 balls, two balls can be drawn in 15C2 ways.
∴  Total number of elementary events = 15C2 = 105

Out of seven white balls, one white ball can be drawn in 7C1 ways; and one ball can be drawn from the rest of the other coloured (red and black) balls in 8C1 ways.
∴ Favourable number of ways = 7C1× 8C1 = 7× 8 = 56
Hence, required probability = $\frac{56}{105} = \frac{8}{15}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 41.3 | Page 48