Question

Two dice are tossed. Find whether the following two events A and B are independent A={(x,y):x+y=11} and B={(x,y):`xne5`}, where (x,y) denotes a typical sample point.

Answer 1

We have, A={(x,y):x+y=11} and B={(x,y):`xne5`}
`therefore` A={(5,6),(6,5)}, B={(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),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
`rArrn(A)=2,n(B)=30and n(AcapB)=1`
`therefore P(A)=2/36=1/18and P(B)=30/36=5/6`
`rArrP(A)cdotP(B)=5/108and P(AcapB)=1/36neP(A)cdotP(B)`
So, A and B are not independent.