chapter_16 - CHAPTER 16 SOLUTIONS AND MINI-PROJECT NOTES...

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CHAPTER 16 SOLUTIONS AND MINI-PROJECT NOTES CHAPTER 16 UNDERSTANDING PROBABILITY AND LONG TERM EXPECTATIONS EXERCISE SOLUTIONS 16.1 a. This statement is an example of a personal probability because it is based on an individual's belief of his/her chances of getting the flu. b. The relative frequency interpretation applies here because this probability is based on repeated observations of the frequency of flu cases each winter. 16.2 a. Assuming that the traits of having red hair and having blond hair are mutually exclusive, Rule 2 can be applied. So the probability of having red hair should be 23% 14% = 9%. b. The probability that a child is living with one parent is the probability that a child is living with just its mother or just its father. Because these two possibilities are mutually exclusive, the probabilities can be added using Rule 2. The answer is 0.247. c. Note that the probability of a birth resulting in more than one child is 0.0301 + 0.0019 = 0.032. So by Rule 1, the probability that a birth will result in only one child is 1 0.032 = 0.968. 16.3 a. This contradicts Rule 1. There are only two possibilities: a person either is wearing a seat belt or is not. So the two probabilities should sum to 1. b. A probability cannot exceed 1. c. This contradicts Rule 4. Red sports cars are a subset of red cars, so the probability that a car is red cannot be less than the probability that it is both red and a sports car. 16.4 a. The probability of not being born on Friday the 13th is 1 1/214 = 213/214, by Rule 1. b. No. For instance, the probability of being born on Friday the 13th if you are born in a year with two is roughly 2/365, whereas if there are three in the year it would be 3/365. c. "The probability of being born on Friday the 13th is 1/214" means that over the long run (many years) 1 in 214 people will be born on a Friday the 13th. 16.5 Explanation 1 is closer to what it means. The number of heads may be far from half for a small number of tosses, so Explanation 2 is incorrect. 16.6 Not all events are repeatable. An example is the probability that the Earth will be uninhabitable by the year 2050. 16.7 a. Because 1/2 the cards are red and 1/2 black, in the long run 1/2 the cards you pick will be black and 1/2 will be red. So whether you guess black or red you have a probability of 1/2 of being right by chance. b. It is a relative-frequency probability because it is based on knowledge of the physical situation, which can be repeated numerous times. c. This would be a personal probability because it is based neither on physical assumptions nor repeated observations, but on a person's belief. d.
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This note was uploaded on 10/15/2011 for the course STAT 100 at Penn State.

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chapter_16 - CHAPTER 16 SOLUTIONS AND MINI-PROJECT NOTES...

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