Three dice are thrown at the same time. Find the probability of getting three two's, if it is known that the sum of the numbers on the dice was 6

Explanation

On a throw of three dice, we have sample space [n(S)]=`6^(3)`=216
Let `E_(1)` is the event when the sum of numbers on the dice was six and `E_(2)` is the event when three two's occurs.
`rArr E_(1)={(1,1,4),(1,2,3),(1,3,2),(1,4,1),(2,1,3),(2,2,2),(2,3,1),(3,1,2),(3,2,1),(4,1,1)}`
`rArrn(E_(1))=10and E_(2)={2,2,2}`
`rArr n(E_(2))=1`
Also, `(E_(1)capE_(2))=1`
`thereforeP(E_(2)//E_(1))=(Pcdot(E_(1)capE_(2)))/(P(E_(1)))=(1//216)/(10//216)=1/10`