Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum  of numbers on the dice is 4’.

Explanation

In a throw of two dice
`n(S)=36`
Let `E=` event of getting different number on both dice
`impliesn(E)=30`
Let `F=` event of getting sum of 4 on both dice
`implies F={(1,3),(2,3),(3,1)}`
`impliesn(F)=3`
Now, `EnnF={(1,3),(3,1)}`
`impliesn(EnnF)=2`
and required probability `=P(F//E)`
`=(P(FnnE))/(P(E))=(2/36)/(30/36)=1/15`