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Question
A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = `1/3` and P(B) = `1/4`. If there are 40 balls in the box which are marked C, find the number of balls in the box.
Solution
P(C) = 1 – [P(A) + P(B)]
= `1 - [1/3 + 1/4]`
= `1- 7/12`
= `5/12`
Probability = `"Number of favorable outcomes"/"Total number of all possible outcomes"`
Given that 40 balls in the box are marked C.
`=> 5/12 = 40/"Total number of all possible outcomes "`
`=>` Total number of all possible outcomes = `(40 xx 12)/5 = 96`
∴ The number of balls in the box is 96.
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