I need help some help with the below problem and would appreciate very much if can offer some help.

thanks

Kingman

John has 5 items, one each to be named P,Q, R,S and T. Each item is placed in a separate

box and sealed. He then addresses the boxes, at random, one each to P,Q,R,S and T.

1) Find the probability that the item P is in the correct box and the letter Q is in the

wrong box. (3/20)

2) Find the probability that the item P is in the correct box, given that the item Q is in the

wrong box.(3/16)

3) Find the probability that both of the items to P and Q are in the wrong boxes.(13/20)

Hint: It would be helpful to draw a Venn diagram showing the various given probabilities.

A suitable tree diagram is also helpful.

Lastly let X denotes the event that X’s item is in the correct box.