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?

Answer 1

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 white marble")=2/9  ..........(1)`

Let the number of white marbles be n.

Then, P(getting a white 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.