Given that `x in [0,1]` and `y in [0,1]`. Let `A` be the event of selecting a point `(x,y)` satisfying `y^(2) ge x` and `B` be the event selecting a point `(x,y)` satisfying `x^(2) ge y`, then

Options

A. `P(AnnB)=(1)/(3)`
B. `AsubB`
C. `2P(A)=3P(B)`
D. `P(B) lt P(A)`

Answer

A

Explanation

`(a)`
`P(A)=(int_(0)^(1)sqrt(x)dx)/(int_(0)^(1)dx)=(2)/(3)` and `P(B)=(int_(0)^(1)sqrt(y)dy)/(int_(0)^(1)dy)=(2)/(3)`
`:. P(AnnB)=(int_(0)^(1)-sqrt(x)dx-int_(0)^(1)x^(2)dx)/(int_(0)^(1)dx)=(2)/(3)-(1)/(3)=(1)/(3)`