A basket contains 4 red , 5 blue and 3 green marbles .
If three marbles are picked at random , what is the probability that at least one is blue ?

Options

A. `(7)/(12)`
B. `(37)/(44)`
C. `(5)/(12)`
D. `(7)/(44)`

Answer

B

Explanation

Total possible outcomes `=n( S) =""^(12)C_(3)=220`
Favourable number of ways of picking 3 marbles (none is blue ) out of 7 marbles
`=""^(7)C_(3)=(7xx6xx5)/(1xx2xx3)=35`
`implies ` Required probability
`=(1-(35)/(220))=(1-(7)/(44))=(37)/(44)`