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?

Answer

N/a

Explanation

Total marbles `=10+20+30=60`
No. of ways of selecting 5 marbles from 60 marbles
`=.^(60)C_(5)`
(i) No. of ways of selecting 5 blue marbles from 20 blue marbles
`=.^(20)C_(5)`
`:.` Required probability `=(.^(20)C_(5))/(.^(6)C_(5))`
(ii) No. of ways of selecting 5 marbles form 20 blue `+10` red marbles `=.^(30)C_(5)`
There will be no green marble in these selections
`:.` Probability that no green marble is selected
`=(.^(30)C_(5))/(.^(60)C_(5))`
`implies` Probability of selecting at least one green marble
`=1-(.^(30)C_(5))/(.^(60)C_(5))`