Two dice are thrown together and the total score is noted. The event E, F and G are a total 4, a total of 9 or more, and a total divisible by 5, respectively. Calculate `P(E),P(F)a n dP(G)` and decide which pairs of events, if any, are independent.

Explanation

Two dices are thrown together i.e., sample spaces (S) =36`rArr`n(S)=36
E=A total of 4 = {(2,2),(3,1),(1,3)}
`rArr n(E )=3`
F= A total of 9 or more
`={(3,6),(6,3),(4,5),(4,6),(5,4),(6,4),(5,5),(5,6),(6,5),(6,6)}`
`rArr n(F)=10`
G =a total divisible by `5={(1,4),(4,1),(2,3),(3,2),(4,6),(6,4),(5,5)]}`
`rArrn(G)=7`
Here, `(EcapF)=phiand (EcapG)=phi`
Also, `(FcapG)={(4,6),(6,4),(5,5)}`
`rArr n(FcapG)=3 and (EcapFcapG)=phi`
`therfore P(E)=(n(E))/(n)(S))=10/36=5/18`
`P(G)=(n(G))/(n(S))=7/36`
`P(FcapG)=3/36=1/12`
and `P(F)cdotP(G)=5/18cdot7/36=35/648`
Her, we see that `P(FcapG)neP(F)cdotP(G)`
[since, only F and G have common events, so only F and G are used here]
Hence, there is no pair which is independent