Refer to question 1 above. If the die were fair, determine whether or not the events A and B are independent.

Explanation

Referring to the above solution, we have
A={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
`rArr n(A)=6andn(S)=6^(2)=36` [where, S is sample space]
`thereforeP(A)=(n(A))/(n(S))=6/36=1/6`
Also, `AcapB={(5,5),(6,6)}`
`rArr n(AcapB)=2 and n(S)=36`
`therefore P(AcapB)=2/36=1/18`
Also, `P(A)cdotP(B)=1/36`
Thus, `P(AcapB)neP(A)cdotP(B)`
So, we can say tehat both A and B are not independent events.