Question

A bag contains 5 white and some black balls. If the probability of drawing a black ball from the bag is twice the probability of drawing a white ball then find the number of black balls.

Answer 1

Let the number of black balls be “x”

Sample space (S) = x + 5

n(S) = x + 5

Let A be the event of drawing a black ball

n(A) = x

P(A) = `("n"("A"))/("n"("S")) = x/(x + 5)`

Let B be the event of getting a white ball

n(B) = 5

P(B) = `("n"("B"))/("n"("S")) = 5/(x + 5)`

By the given condition,

`x/(x + 5) = 2 xx (5/(x + 5))`

⇒ `x/(x + 5) = (10/(x + 5))`

⇒ 10x + 50 = x² + 5x

⇒ x² + 5x – 10x – 50 = 0

⇒ x² – 5x – 50 = 0

⇒ (x – 10)(x + 5) = 0

⇒ x = 10 or x = – 5

Number of balls will not be negative.

Number of black balls = 10