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 the number of black balls in the bag be x.
Since the number of red balls is three more than black balls, the number of red balls is x + 3.

Total balls = x + (x + 3)

= 2x + 3

The probability of drawing a red ball is given as `12/23`; so, 

`"Number of red balls"/"Total number of balls" = 12/23`

Substituting values,

Probability of drawing a red ball = `12/23`

⇒ 24x − 36 = 23x

⇒ 24x − 23x = 36

⇒ x = 36

∴ Number of black balls = x − 3 

= 36 − 3

= 33

∴ Total number of balls in the bag = 36 + 33

= 69