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?
No. of red marbles = 10
No. of blue marbles = 20
No. of green marbles = 30
Total number of marbles = 10 + 20 + 30 = 60
Number of ways of drawing 5 marbles from 60 marbles = 60C5
(i) All the drawn marbles will be blue if we draw 5 marbles out of 20 blue marbles.
Number of ways of drawing 5 blue marbles from 20 blue marbles = 20C5
Probability that all marbles will be blue = 20C5 / 60C5
(ii) Number of ways in which the drawn marble is not green = (20+10)C5
Probability that no marble is green = 30C5 / 60C5
Probability that at least one marble is green = 1 - 30C5 / 60C5