Now suppose Streak-Shooting Shelly has moved to mars. Shelly is still adjusting to Mars. Her overall performance is down, but she still shoots better when she has just made a shot.
Suppose Shelly has a 60% probability of making the first shot. If she gets the first shot, she has an 80% probability of making the second shot. If she gets the first two shots, her probability of making the third shot rises to 90%. How many pints is shelly most likely to scorn one-and-one-and-one situation?
To determine how many points Shelly is most likely to score in a one-and-one-and-one situation, we'll calculate the probabilities of making each shot and multiply them by the respective number of points each shot is worth.
In a one-and-one-and-one situation, Shelly has three shots. Let's consider each shot individually:
Shot 1: Shelly has a 60% probability of making this shot, so the expected number of points earned from this shot is 0.6 × 2 = 1.2 (assuming each made shot is worth 2 points).
Shot 2: If Shelly makes the first shot, she has an 80% probability of making the second shot. So the expected number of points earned from this shot, given that she made the first shot, is 0.8 × 2 = 1.6.
Shot 3: If Shelly makes the first two shots, her probability of making the third shot rises to 90%. So the expected number of points earned from this shot, given that she made the first two shots, is 0.9 × 2 = 1.8.
To calculate the overall expected number of points earned in a one-and-one-and-one situation, we sum up the expected points for each individual shot:
Expected points = (Probability of making Shot 1 × Points earned from Shot 1) + (Probability of making Shot 1 and Shot 2 × Points earned from Shot 2) + (Probability of making all three shots × Points earned from Shot 3)
Expected points = (0.6 × 1.2) + (0.6 × 0.8 × 1.6) + (0.6 × 0.8 × 0.9 × 1.8)
Simplifying the above equation will give us the expected number of points Shelly is most likely to score in a one-and-one-and-one situation.