Events A and B are such that `P(A)=1//2,P(B)=7//12,` and P (not A or not B) = 1/4. State whether A and B are independent ?

Answer

N/a

Explanation

Given `P` (not A or not B)`=1/4`
`impliesP(A' "or"B')=1/4`
`impliesP(A'uuB')=1/4impliesP(AnnB)'=1/4`
`[ :' P(A'uuB')=P(AnnB)']`
`implies1-P(AnnB)=1/4impliesP(AnnB)=1-1/4=3/4`
Now, `P(A)xxP(B)=1/2xx7/12=7/24!=3/24`
[Given `P(A)=1/2, P(B)=7/12]`
`impliesP(A)xxP(B)!=P(AnnB)`
`:.` Events A and B are not independent events.