Q. 245.0( 1 Vote )

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) and P(G) and decide which pairs of events, if any, are independent.

Answer :

We are throwing two dice so,


Sample space S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),


(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),


(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),


(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),


(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),


(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}


Sample space contains 36 elements,


n(S)=36


let E be an event of getting sum 4


E={(1,3),(3,1),(2,2)}


n(E)=3



F be the event of getting 9 or more


F ={(3,6),(6,3),(4,5),(5,4),(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)}


n(F)=3



G be the event getting a total divisible by 5


G= {(1,4),(4,1),(2,3),(3,2),(4,6),(6,4),(5,5)}


n(G)=7



So E and F are not independent


So E and G are not independent




So F and G are not independent


Therefore no pair is independent


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