Question

Consider two events such that P(A)=1/6,P(B)=3/5, and P(AnB)=1/10. Are events A and B independent events

Answer 1

We are given

`P(A)=(1)/(6)`

`P(B)=(3)/(5)`

P(A∩B)=
`(1)/(10)`

Two events A and B are independent when

P(A∩B)=
`P(A)*P(B)`

so, we can plug values and check it

`(1)/(10) =(1)/(6) *(3)/(5)`

now, we can simplify right side

`(1)/(10) =(3)/(6*5)`

`(1)/(10) =(1)/(10)`

we can see that

both sides are equal

so, events A and B are independent .............Answer