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Q.

A bag contains 8 red balls and some blue balls. If the probability of drawing a blue ball is three times of a red ball, then the number of blue balls in the bag is:

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a

18

b

8

c

24

d

20

answer is C.

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Detailed Solution

Given, a bag contains 8 red balls and some blue balls. If the probability of drawing a blue ball is three times of a red ball.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an event = Number of favourable cases Total number of cases

Find the total number of balls in the bag.
Consider that there are x number of blue balls in the bag.
So, the total number of balls in the bag is

x + 8

also, consider that probabilities of drawing a blue ball and drawing a red ball be

P 1

and

P 2

respectively.
So,

P 1 = x x + 8 and P 2 = 8 x + 8

.
Find the required value of x: by using the equation

P 1 = 3 P 2 x x + 8 = 3 × 8 x + 8 x (x + 8) = 24 (x + 8) x = 24

Thus, the required value of

x

is 24.
So, the number of blue balls in the bag is 24.
Hence, the correct option is 3.

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A bag contains 8 red balls and some blue balls. If the probability of drawing a blue ball is three times of a red ball, then the number of blue balls in the bag is: