Answers to the Review questions Chapter 16

1. iii
2. i
3. both are wrong.  Luck and the law of averages have nothing to do
with it, the chances will remain unchanged no matter how many
times.
4. (a) 60 rolls, with more rolls, the percentage of ones will be
closer to 16.67.  But you want the percentage to far away from
16.67%  So, choose the smaller number of rolls.
(b) 600 rolls, now you want to be closer to 16.67.
(c) 600 rolls, just like b
(d) 600.  Here, you  want the long-run average which is 16.67% and
you are more likely to get it with more rolls.
5.  False.  If the number of heads is 50, the percentage is 50.
6. (i) is better.  Reasoning: 10/15  = 2/3.  Option i is like 
tossing a coing 15 times and looking for > 2/3 heads. 
7.  It's 25 draws from a box with one +4 and four -1
8.  The net gain is like the sum of 50 draws from a box with four
tickets with a +8 and 34 with a -1.
9.  Choose (ii).  More draws means the percentage of reds will be
most like the percentage in the box. Review exercise 4 above. 
10.  (a) 30/200 = .15
(b) -0.1
(c) average = sum/200
(d) 5/200 = .025