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Question
A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probability of selecting a blue marble at random is `1/3` and the probability of selecting a green marble at random is `4/9`. How many white marbles does the jar contain?
Solution
Total number of marbles = 54.
It is given that, P(getting a blue marble) = `1/3` and P(getting a green marble) =`4/9`
Let P(getting a white marble) be x.
Since, there are only 3 types of marbles in the jar, the sum of probabilities of all three marbles must be 1.
`therefore 1/3 + 4/9 + x = 1 `
`⇒ (3 +4)/9 + x = 1`
`⇒ x = 1 - 7/9`
`⇒ x = 2/9`
`therefore P("getting a while marble")=2/9 ..........(1)`
Let the number of while marbles be n.
Then, P(getting a while marble) =`n/54 ........(2)`
From (1) and (2),
`n/54 = 2/9`
`rArr n = (2xx54)/9`
⇒ n = 12
Thus, there are 12 white marbles in the jar.
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