box item problem
I need help some help with the below problem and would appreciate very much if can offer some help.
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
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.
Thanks very much for the neat and clear answer. However my main problem is how to express the outcomes,events and probabilities in the Venn diagrams or tree diagram. I wonder how I can express the solution in the form of P(Q|P),using intersection and union symbols.
Thank you very much.