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Question:

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

Solution:

Let total number of balls in jar = x
Then number of blue balls in jar = (1/3)x = x/3
And number of red balls = (1/4)x = x/4
And number of orange balls = 10 (given)
∴ x = x/3 + x/4 + 10
⇒ 12x = 3x + 4x + 120
⇒ 12x - 7x = 120
⇒ 5x = 120
⇒ x = 24
Then total balls in jar is 24.