Stat 1040
Chapter 16 Solutions

  1. Option (iii) is the best because the chance error is not likely to be exactly zero, but it is likely to be small compared to the number of draws.

  2. Both are wrong. Luck and the law of averages are irrelevant because each spin is independent of those that go before. The chances stay the same.

    1. 60 rolls. To win, you need a large percentage error, and that is more likely in 60 rolls.
    2. 600 rolls - now you want a small percentage error.
    3. 600 rolls again - you want a small percentage error.
    4. 60 rolls because to get exactly the expected value means getting exactly zero chance error, and that is more likely with fewer rolls.

  4. Possibility (i) is more likely because you want the percentage error to be at least 66 2/3% - 50% = 16 2/3%. The percentage error is more likely to be at least 16 2/3% in the short run.

  5. The score is like the sum of 25 draws from a box with one ticket marked "4" and 4 tickets marked "-1".

  6. The net gain is like the sum of 50 draws from a box with 4 tickets marked "$8" and 34 tickets marked "-$1".

  7. Option (ii) is the best. Say the percentage of reds in the box is 60%. Then to win, we want the percentage error to be small, so that the actual percentage will be greater than 50%. This is more likely in the long run.

    1. 30/200 = 0.15.
    2. -20/200 = -0.1.
    3. average = sum/200.
    4. They are the same because 5/200 = .025.