Chapter 16 Exercises
1. Suppose you flip a fair coin repeatedly. Which gives you a better chance of getting
more than 70% heads, 50 flips or 500 flips?
2. I offer you the following game: we each roll a die, and if you get strictly more than me
on your roll, you win $1. Otherwise, you lose $1. Is it in your best interest to play 1, 10,
or 100 times? Why?
3. Suppose you roll a fair die 24 times.
a) How many 6’s do you expect to see?
b) Suppose that you do not roll any 6’s in the 24 rolls. What is the probability that the
next roll will be a 6?
4. Suppose you draw with replacement from the box 0 1 1 .
a) What is the probability of drawing a 1 on a given play?
b) If you win $50 by drawing less than 50% 1’s, would you be better off to play 10 or
100 times?
c) If you win $50 by drawing less than 70% 1’s, would you be better off to play 10 or
100 times?
(4) d) If you win $50 by drawing between 60% and 70% 1’s (inclusive), would you be
better off to play 10 or 100 times?
For Problems 5-8, draw a box model appropriate to the scenario, and state the
appropriate number of draws.
5. You roll a fair 6-sided die 10 times and record the outcomes.
6. You roll a fair 6-sided die 25 times and count the number of aces.
7. You roll a fair 6-sided die 5 times. You win $4 if you roll an ace, you lose $1
otherwise.
8. You roll a green die and a red die together 10 times and count the number of times the
green die shows more spots than the red die.
9. Suppose you draw from the box 1 2 3 4 5 6 7 a total of 70 times.
a) What is the largest value the sum total can be? The smallest?
b) What is the average of the box?
c) What might you expect the sum to be?
10. If five draws are made from the box 1 2 4 6 8 , what is the probability that you
draw all even numbers:
a) If the draws are made without replacement?
b) If the draws are made with replacement?