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) at least one will be green.

Answer 1

Total number of marbles = 10 + 20 + 30 = 60
Number of ways of drawing 5 marbles from 60 marbles =$^{60}C_5$

(i) All the drawn marbles will be blue if we draw 5 marbles out of 20 blue marbles.
5 blue marbles can be drawn from 20 blue marbles in $^{20}C_5$ways.
∴Probability that all marbles will be blue =$\frac{^{20}C_5}{^{60}C_5}$

(ii) Number of ways in which the drawn marble is not green =$^{(20+10)}C_5=\space^{30}C_5$
∴Probability that no marble is green =$\frac{^{30}C_5}{^{60}C_5}$
∴Probability that at least one marble is green =$1- \frac{^{30}C_5}{^{60}C_5}.$