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Question
The probability of selecting a red ball at random from the 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
It is given that,
P(getting a red ball) =`1/4` and P(getting a blue ball) =`1/3`
Let P(getting an orange ball) be x.
Since, there are only 3 types of balls in the jar, the sum of probabilities of all the three balls must be 1.
`therefore 1/4 + 1/3 + x = 1`
`rArr x = 1 - 1/4 -1/3`
`rArr x = (12-3-4)/12`
`rArr x = 5/12`
∴ P(getting an orange ball) =`5/12`
Let the total number of balls in the jar be n.
∴ P(getting an orange ball) = `10/n`
`rArr 10/n = 5/12`
`rArr n = 24`
Thus, the total number of balls in the jar is 24.
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