1) Assume there are three traffic lights between your house and a friend's house. As you arrive at each light it may be red (R) or green or yellow (lump them both together as G).

1. List the sample space showing all possible sequences of red and green lights that could occur on a trip from your house to your friend's. (RGG represents red at the first for example.)

2. Assume that each light is equally likely to be G or R. Give the probability of each sample point.

3. Assume that the first two lights are equally likely to be G or R, but the last has a 75% chance of being R. Give the probability of each sample point.

4. Are sample points mutually exclusive events? Explain.

5. Are sample points independent events? Explain.

 
2) Consider a standard deck of playing cards and the act of drawing two cards (without replacement).

1. What is the probability of drawing two kings?

2. Of drawing a king and a queen?

 
3) Scoring a hole-in-one is the single greatest shot a golfer can make. Golf Digest (1990) reports that the estimated probability of making a hole-in-one is 1/2,970 for a male professional golfer. Suppose we randomly select four male professional golfers and a typical hole at a PGA golf course.

1. What is the probability that the first two golfers both get a hole in one? What do you need to assume to get this answer?

2. What is the probability that all four golfers get a hole in one?

3. What is the probability that the first golfer does not get a hole in one?

4. What is the probability that none of the four golfers gets a hole in one?

5. What is the probability that at least one of these four golfers got a hole in one?

6. In the 1989 U.S. Open, four players each made holes-in-one on the sixth hole at Oak Hill Country Club. Do you think the probability of a hole-in-one on the sixth hole at Oak Hill Country Club is the same as the probability reported by Golf Digest? Why, or why not?