A bucket contains 8red,3 blue and 5 green marbles .
If 3 marbles are drawn at random , what is the probability that none is red ?

Options

A. `(3)/(8)`
B. `(1)/(16)`
C. `(1)/(10)`
D. `(3)/(16)`

Answer

C

Explanation

`n(S) =""^(16)C_(3) =(16xx15xx14)/(1xx2xx3)=560`
Out of the three drawn marbles none is red clearly they will be either blue or green .
`implies n( E)=""^(8)C_(3)=(8xx7xx6)/(1xx2xx3)=56`
`implies ` Required probability `=(n( E))/(n(S))=(56)/(560)=(1)/(10)`