Question

What does it mean about events `A` and `B` if `P(A|B)=P(B|A)`?

Answer 1

Probabilities of event `A` and `B` are same.

Explanation:

Note that

`P(A|B)= P(B|A)`
`implies (P(A nn B) )/(P(B))=(P(A nn B))/(P(A))`
`implies P(A) = P (B)`

So we can conclude probabilities of event `A` and `B` are same.