A box contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that the selected ball is not red?
- \(\frac 16\)
- \(\frac 12\)
- \(\frac 13\)
- \(\frac 56\)
The Correct Option is D
Solution and Explanation
Let $R$ be the number of red balls, $W$ be the number of white balls, and $B$ be the number of blue balls.
We are given that $R = x$, $W = 2x$, and $B = 3x$.
The total number of balls in the box is 24. So, $R + W + B = 24$.
Substituting the given values, we have $x + 2x + 3x = 24$ $6x = 24$ $x = \frac{24}{6} = 4$
Thus, $R = 4$, $W = 2(4) = 8$, and $B = 3(4) = 12$.
We want to find the probability that the selected ball is not red.
This means the selected ball is either white or blue.
The number of balls that are not red is $W + B = 8 + 12 = 20$.
The probability of selecting a ball that is not red is the number of non-red balls divided by the total number of balls: $$ P(\text{not red}) = \frac{\text{Number of non-red balls}}{\text{Total number of balls}} = \frac{W + B}{24} = \frac{20}{24} = \frac{5}{6} $$
The probability that the selected ball is not red is $\frac{5}{6}$.
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