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, S the event of picking the white ball in the second drawing.

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