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Question
A bag contains 8 red and some blue balls. One ball is drawn at random from the bag. If ratio of probability of getting red ball and blue ball is 2:5, then find the number of blue balls.
Solution
Suppose the number of blue balls = x
∴ n(Blue ball) = x
Number of red balls = 8
∴ n(Red ball) = 8
Total number of balls = 8 + x
∴ n(T) = 8 + x
P(Blue ball drawn) = `(n("Blue ball"))/(n(T))`
= `x/(8 + x)`
P(Red ball drawn) = `(n("Red ball"))/(n(T))`
=`8/(8 + x)`
According to the given condition
`(P("Blue ball drawn"))/(P("Red ball drawn")) = 5/2`
∴ `x/((8 + x)/8) = 5/2`
∴ `x/8 = 5/2`
∴ x = 20
Hence, the number of blue balls is 20.
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