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Question
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is `2/5`, find the number of red balls in the bag.
Solution
The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is 4 + x .
Let A be the event of drawing a white ball.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P (A) and is given by
` P (A) = m/n`
Therefore, we have `P(A) = 4/(4+x)`.
But, it is given that ` P (A) = 2/5` . So, we have
` 4/(4+x) =2/5`
⇒2(4 + x ) = 20
⇒ 8 + 2x = 320
⇒ 2x = 20-8
⇒2x = 12
⇒ x =`12/6`
⇒ x =6
Hence the number of red balls is 6 .
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