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

Options

A. `(7)/(4)`
B. `(7)/(12)`
C. `(5)/(12)`
D. `(1)/(44)`

Answer

D

Explanation

Total possible outcomes =Number of ways of picking 3 marbles out of 12 marbles `=n(s)`
`=12_(C_(3))(12xx11xx10)/(1xx2xx3)=220`
Favourable number of cases `=n( E)`
`=""^(3)C_(3)+""^(4)C_(3)`
`=1+4=5`
`implies ` Required probability
`=(n( E))/(n(S))=(5)/(220)=(1)/(44)`