3.2 Exercise 17

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Let T be the event of getting the white ball twice, F the event of picking the white ball first, and S the event of picking the white ball in the second drawing.

1. Compute P(T).
2. Compute P(T|F).
3. Are T and F independent?
4. Are F and S mutually exclusive?
5. Are F and S independent?