Look at two definitions first: mutual exclusion: if A∩B is an impossible event (a ∩ b = φ),

Opposition: if A∩B is an impossible event (a ∩ b = φ), P(A)+P(B)= 1

Obviously, we can see mutual exclusion: two can't happen at the same time, but there is no probability relationship between them, and maybe neither of them will happen.

For example, there are red, white and black balls in the bag. The first time I got the white ball and the first time I got the red ball was mutually exclusive events. It can't happen at the same time, but there are other possibilities (getting the black ball)

Opposition: two can't happen at the same time, but it's either A or B. For example, there are only red and white balls in the bag. Then, "getting the white ball for the first time" and "getting the red ball for the first time" are opposite events. Can't happen at the same time, but it is either a white ball or a red ball.

You got it? Contradictory events belong to a special kind of mutually exclusive events. Opposing events are all mutually exclusive events, but mutually exclusive events is not necessarily an opposing event.