Tom and Jerry are playing hide and seek.

They have only two hiding places, in the wardrobe or under the stairs. It takes one minute to find out if someone is hidden in the wardrobe (there are a lot of old coats) and two minutes to find out if someone is hidden under the stairs (there are a lot of old cardboard boxes).

Jerry hides in one of the hiding places and then Tom searches until he finds him. 

Jerry chooses to hide under the stairs with probability 0.3 and Tom chooses to search under the stairs first with probability 0.6.

What is the probability that Tom finds Jerry in two minutes or less?

On average, how long will it take Tom to find Jerry?

If Jerry wants to maximise the time it takes Tom to find him, where should he hide?

If we generalise and say that Jerry chooses to hide under the stairs with probability p and Tom chooses to search under the stairs first with probability q, what will these answers to these questions be?