1.

If `A and B` are independent events of a random experiment such that `P(A nn B) = 1/6 and P( overlineA nn overlineB)=1/3` then `P(A)=`A. `(1)/(4)`B. `(1)/(3)`C. `(1)/(6)`D. `(2)/(3)`

Answer» Correct Answer - B
We have,
`P(A cap B)=(1)/(6) " and " (overline(A) cap overline (B))=(1)/(3)`
`implies P(A) P(B)=(1)/(6) " and " P(overline(A))P(overline(B))=(1)/(3)`
`implies xy=(1)/(6) " and" (1-x)(1-y)=(1)/(3)`, where P(A)=x, P(B)=y
`implies xy=(1)/(6) " and " 1-x-y+(1)/(6)=(1)/(3)`
`implies xy=(1)/(6) " and " x+y=(5)/(6)`
`implies x=(1)/(2) " and " y=(1)/(3) " or" x=(1)/(3) " and " y=(1)/(2)`


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