A) Suppose that an experiment consists of flipping a coin three times. The event A is defined as "the first and the third flips are heads", and the event B is defined as "no heads turn up."

1) Compute P(A)

2) Compute P(B)

3) Compute P(A U B)

4) Compute P(A ? B)

5) Compute P(A^C)

6) Compute P(B^C)

7) Compute P(A|B)

8) Compute P(B|A)

9) Are A and B mutually exclusive events? Why or why not?

10) Are A and B independent events? Why or why not?

11) Are A and B complements? Why or why not?

B) Find the derivative of: