Question

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random from the bag is three times that of a red ball, find the number of blue balls in the bag.

Answer 1

Let number of blue balls in the bag = x

Total no. of balls in bag = 5 + x   ...[∵ No. of red balls = 5]

Probability of drawing a blue ball

= `"No. of blue balls"/"Total no. of balls"`

i.e., P(B) = `x/(5 + x)`

Probability of drawing a red ball

= `"No. of red balls"/"Total no. of balls"`

i.e., P(R) = `5/(5 + x)`

Given, P(B) = 3P(R)

∴ `x/(5 + x) = 3(5/(5 + x))`

x = 3 × 5

x = 15

Hence, number of blue balls in the bag = 15.