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Question:

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

Solution:

Let there be x blue balls.
So, the total number of balls = x + 5
P(Blue ball) = x/(x+5)
P(Red ball) = 5/(x+5)
Given, P(Blue) = 2 × P(Red)
x/(x+5) = 2 × 5/(x+5)
Solving, we get x as 10.
So, the number of blue balls = 10.