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Question

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?

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Solution

Let a box contains 10red marbles, 20blue marbles and 30green marbles. 5 marbles are drawn from box.

Total number of marbles in the box is 60.

The total number of ways of drawing 5marbles from 60marbles is 60 C 5 .

(i)

Given, all the marbles drawn will be blue.

According to question all marbles will be blue if we draw 5marbles out of 20blue marbles that is 20 C 5 .

Thus, the probability for all marbles will blue is,

P= 20 C 5 60 C 5

(ii)

Given, at least one will be green.

The number of ways in which drawn marbles is not green is ( 20+10 ) C 5 .

The probability that no marble is green is,

P= ( 20+30 ) C 5 60 C 5 = 30 C 5 60 C 5

Thus, the probability that at least one will be green is ( 1 30 C 5 60 C 5 ).


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