Question

Suppose `Q` and `R` are independent events. What is `P(Q` and `R`) if `P(Q) = 7/15` and `P(R)=4/7`?

Answer 1

If `Q` and `R` are two independent events,
then `P(Q and R)=P(Q)xxP(R)=4/15` - however there is an issue.

Explanation:

If `Q` and `R` are two independent events, then

`P(Q and R)=P(Q)xxP(R)`

and hence in the given instant

`P(Q and R)=7/15xx4/7=4/15`

However, in the given case it is observed that

`P(Q)+P(R)=7/15+4/7=(7xx7+15xx4)/(15xx7)=109/105`

this is greater than one, meaning thereby that `Q` and `R` are not independent event.