You are given a jar containing n 12 marbles 5 of which are

You are given a jar containing n = 12 marbles, 5 of which are Red and 4 are White and 3 are Black. You randomly slect 3 marbles from the jar totally at random (without replacement).

a) Find the probablity the exactly 2 red and 1 white

Solution

You are given a jar containing n = 12 marbles, 5 of which are Red and 4 are White and 3 are Black. You randomly select 3 marbles from the jar totally at random (without replacement).

a) Find the probability the exactly 2 red and 1 white

Three possibilities RRW,RWR,WRR

first marble red =5/12

second marble red =4/11

third white =4/10

P( RRW) = (5*4*4)/(12*11*10) =2/33

Similarly P( RWR)=2/33

P(WRR)=2/33

The required P = 2/33+2/33+2/33 =2/11