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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 - Mathematics

Short Note
Sum

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?

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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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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 15 Probability
Exercise 15B | Q 13 | Page 697
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