Question

The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is `12/23`, find the total number of balls in the given bag.

Answer 1

Let number of black balls = x

Number of red balls = x + 3

So, Total number of balls = 2x + 3

Given, P(drawing a red ball) = `12/23`

⇒ `(x + 3)/(2x + 3) = 12/23`

⇒ 23x + 69 = 24x + 36

⇒ 69 − 36 = 24x − 23x

∴ x = 33

Total number of balls = 2x + 3

= 2 × 33 + 3

= 66 + 3

= 69 balls