Question

a bag contains 3 red and some blue balls. If the probability of drawing a blue ball is four times that drawing a red ball, find the number of blue balls in the bag

Answer 1

The number of blue balls in the bag is 12

We will call the amount of blue balls "n"

The total of balls is: 3 + n

The probability of drawing a red ball:

P(R) = 3/(3+n)

The probability of drawing a blue ball:

P(A) =n/(3+n)

If the probability of drawing a blue ball is four times that drawing a red ball, we have to:

P(A) = 4P(R)

⇒ P(R) = P(A)/4

Substituting:

P(A)/4 = 3/(3+n)

P(A) = 12/(3+n)

Substituting:

12/(3+n) = n/(3+n)

n = 12

The number of blue balls in the bag is 12.