1. You roll two dice. Let A be the event that they land on the same number, and let B be the event that at least one lands on 6. What is P(B|A^c )?

2. Let C be a random variable indicating the sum of two dice. Find: P[First die = 6|C = c] Compute for c equals 4 through 8.

3. A car insurance company insures four types of drivers:

Good drivers who have a 1% chance of getting in an accident each year

Mediocre drivers have a 5% chance of getting in an accident in each year

Atrocious drivers who have a 35% chance of getting in an accident in each year

Ludicrously bad drivers who have a 90% chance of getting in an accident each year

50% of drivers are good, 35% are mediocre, 12% are atrocious, and 3% are ludicrously bad. A driver they insure gets in an accident, what is the likelihood he is a good, mediocre, atrocious, or ludicrously bad driver.

4. Identify the independent events:

P(A) = .5 P(B) = .5 P(A B) = .75

P(C) = .2 P(D) = .8 P(C D) = .16

P(E) = .4 P(F) = .5 P(E^c F^c ) = .3

5. I roll one die, let A be the event I roll a perfect square (i.e. 1 or 4) and B be the event I roll an even number. Are A and B independent?

6. I roll two dice, let A be the event I roll a perfect square (i.e. 1, 4, or 9) and B be the event I roll an even number. Are A and B independent?