HOMEWORK #3 ANSWERS
Chapter 13
6. (a) True.
(b) True. See example 2 on p. 226.
(c) False. The two events are dependent. See example 4 on p.229. The chance is 1/52 x 1/51, not 1/52 x 1/52.
7. (a) False.
(b) False.
(c) True.
Both sequences are equally likely, having chance 1/26. Of course, there are a lot more sequences with 3 heads and 3 tails, but that's not the question.
10. Box (ii) is better, there is more of a chance to get the 5. With box (ii), you will get
around 50 1's and 50 5's, so you will make around $300. Not bad.
12. 3/100 x 2/99 x 1/98 » 6/1,000,000
Chapter 14
4. Option (i) is better. Even if you miss the first time, you get a second try at the
money.
6. If you want to find the chance that at least one of the two events will happen, check to see if they are mutually exclusive; if so, you can add the chances. If you want to find the chance that both events will happen, check to see if they are independent; if so, you can multiply the chances.
13. By trial and error, (0.98)34 » 0.503, and (0.98)35 » 0.493. With 34 draws, there is a 49.7% chance of getting a red marble; with 35 draws, the chance is 50.7%. The answer is 35. (Logs are a more sophisticated option.)
Chapter 15
3. The chance of getting 4 girls is (I/2)4 = 1/16. The chance of getting 3 girls is 4/16,
by the binomial formula; the total chance is 5/16, by the addition rule.
6. False: 8!/(2!6!) = 8!/(6!2!)
8. The chance of getting 2 heads among the first 5 tosses is :
The chance of getting 4 heads among the last 5 tosses is: 
The first 5 tosses are independent of the last 5. So the answer is:
