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The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is $\frac{1}{4}$ . The probability of selecting a blue ball at random from the same jar is $\frac{1}{3}$ . If the jar contains 10 orange balls, find the total number of balls in the jar.

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answer is A.

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Detailed Solution

Given that, the probability of selecting a red ball at random from a jar that contains only red, blue, and orange balls is

\frac{1}{4} .

For an event A , the probability of an event P(A) is,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

The probability of selecting a blue ball at random from the same jar is

\frac{1}{3}

and the jar contains 10 orange balls.
Let the total number of balls be x .
Therefore, the probability that the randomly drawn ball is a red ball is,

P (A) = \frac{Number of red balls}{Total number of balls}

\Rightarrow \frac{1}{4} = \frac{Number of red balls}{x}

Number of red balls

= \frac{x}{4}

The probability that the randomly drawn ball is a blue ball is,

P (B) = \frac{Number of blue balls}{Total number of balls}

\Rightarrow \frac{1}{3} = \frac{Number of blue balls}{x}

Number of red balls

= \frac{x}{3}

Since the total number of balls is x ,

\Rightarrow \frac{x}{4} + \frac{x}{3} + 10 = x

\Rightarrow \frac{3 x + 4 x}{12} + 10 = x

\Rightarrow 5 x = 120

\Rightarrow x = 24

The total number of balls is 24.
Hence, option 1 is the correct answer.

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