InterviewSolution
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InterviewSolution
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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 by5, respectively. Calculate `P(E),P(F)a n dP(G)`and decide which pairs of events, if any, are independent. |
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Answer» 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 |
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