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A bag contains 24 balls of which x are red, 2x are white, and 3x are blue. A ball is selected at random. The probability that it is white ____.

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Detailed Solution

A bag contains 24 balls of which x are red, 2x are white, and 3x are blue. A ball is selected at random. The probability that it is white

13

.
Determine the value of x.
Total number of balls is

n S = 24

.
Given that, the bag contains 24 balls of which x are red, 2x are white and 3x are blue. Therefore,

x + 2 x + 3 x = 24 6 x = 24 x = 246 x = 4

Solve further to obtain the number of white and blue balls,

2 x = 2 × 4 2 x = 8

3 x = 3 × 4 3 x = 12

This implies, the number of red balls are 4, the number of white balls are 8, and the number of blue balls are 12.
The number of balls which are white is 8.
The probability is,

P A = Number of balls which are white Total number of balls P A = 824 P A = 13

Therefore, the required probability is

13

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