Chapter 5 Review

Based on your assessment of the stock market, you state that the chances that stock prices will start to go down within 2 months are This concept of probability based on your beliefs is called a. Classical probability b. Empirical probability c. Subjective probability d. Independence

Based on your assessment of the stock market, you state that the chances that stock prices will start to go down within 2 months are This concept of probability based on your beliefs is called a. Classical probability b. Empirical probability c. Subjective probability d. Independence

A study of absenteeism from the classroom is being conducted. In terms of statistics, the study is called a. An experiment b. An event c. An outcome d. A joint probability

A study of absenteeism from the classroom is being conducted. In terms of statistics, the study is called a. An experiment b. An event c. An outcome d. A joint probability

In a study of absenteeism, the results showed that 126 students were absent from Monday morning classes. This number (126) is called a. An experiment b. An event c. An outcome d. A joint probability

In a study of absenteeism, the results showed that 126 students were absent from Monday morning classes. This number (126) is called a. An experiment b. An event c. An outcome d. A joint probability

To apply this rule of addition, P(A or B)= P(A) + P(B), the events must be a. Joint events b. Conditional events c. Mutually exclusive events d. Independent events

To apply this rule of addition, P(A or B)= P(A) + P(B), the events must be a. Joint events b. Conditional events c. Mutually exclusive events d. Independent events

Management claims that the probability of a defective relay is only The rule used for finding the probability of the relay not being defective is the a. Addition rule b. Multiplication rule c. Complement rule d. Special rule of addition

Management claims that the probability of a defective relay is only The rule used for finding the probability of the relay not being defective is the a. Addition rule b. Multiplication rule c. Complement rule d. Special rule of addition

Management claims that the probability of a defective relay is only The probability of the relay not being defective is a b c d. 1.0

Management claims that the probability of a defective relay is only The probability of the relay not being defective is a b c d. 1.0

Probability Problem Solving Process For each problem Determine what the events are. Decide whether to use the “and” combination, the “or” combination, or the complement rule. Before choosing the correct formula, ask one of the following questions: 1.For the AND combination: are the events independent? 2.For the OR combination: are the events mutually exclusive? Write down the appropriate formula.

a. If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? b. Assign probabilities to the outcomes of the sample space in part a. Do the probabilities add up to 1? c. What is the probability of getting a number less than 5 on a single throw? d. What is the probability if getting 5 or 6 on a single throw?

a. The sample space consists of equally likely outcomes of {1,2,3,4,5,6} b. Assign each of the 6 outcomes a probability of 1/6. Probabilities add up to: 1/6+1/6+1/6+1/6+1/6+1/6=6/6=1 c. Being successful in getting a number less than 5 on a single throw can be achieved by getting a 1 or a 2 or a 3 or a 4. Since there are 4 ways of being successful out of 6 possible ways, the probability is 4/6 (or 2/3). d. Since there are 2 ways (rolling a 5 or a 6) of being successful out of the 6 possible ways, the probability of getting a 5 or a 6 on a single throw is 2/6 or 1/3.

Two marbles are drawn without replacement from a bowl containing 7 red, 4 blue, and 9 yellow marbles. 1. What is the probability that both are red? 2. What is the probability neither is red? 3. What is the probability at least one is red?

1. (both red) a) Events are: A= first marble is red B= second is red b) This is an “and” combination (1 st & 2 nd are red). c) To determine the correct formula, we need to know “are the events independent or dependent?” d) The events are dependent since the 1 st marble is not replaced before the 2 nd is drawn. e) Use the formula P(A and B)= P(A)P(B|A) P(1 st is red)=P(A)= 7/20; P(2 nd is red, given 1 st is red)= P(B|A)= 6/19 P(A and B)= (7/20)(6/19)=.1105

2. (neither red) a) This is an AND combination: the 1 st is not red and the 2 nd is not red. b) The events are dependent since the 1 st marble is not replaced before the drawing the 2 nd. c) P(1 st not red)= P(A)= 13/20; P(2 nd not red, given 1 st not red)= P(B|A)= 12/19 d) Using the multiplication rule: P(neither is red)= (13/20)(12/19)=.4105

3. (at least one red) a) The complement to “at least one is red” is “neither”. b) Using the complement rule: P(at least 1 is red)= 1-P(neither is red) = =.5895

2 dice are rolled and the sum of the dice is noted. 4. What is the probability the sum is a 7 or 11? 5. What is the probability it is at least a ten? 6. What is the probability the sum is less than a ten?

4. (sum 7 or 11) a) This is an OR combination. b) The events are mutually exclusive, since a roll cannot be both a 7 and an 11 at the same time. c) Use the simple addition rule: P(A or B)= P(A) + P(B) P(7 or 11)= (6/36) + (2/36)=.2222

5. (sum at least 10) a) This is an OR combination. At least a 10 means 10 OR 11 OR 12. These 3 outcomes are mutually exclusive, so we may add the probabilities. b) P(at least a 10)= 3/36 + 2/36 + 1/36 = 6/36 =.1667

6. a) This is the complement to number 5 above. b) P(less than 10)= 1- P(at least 10) = =.8333

Respondents in 3 cities were asked whether they would buy a new breakfast cereal that was being taste tested. Use the responses from the contingency table to answer the questions. Fort Worth DallasChicagoTotal Yes No Undecided Total

7. What is the probability a person responded yes? Total in Yes row is 400 and in sample is Probability a person responded yes is 400/1000=.4

8. What is the probability a person is from Dallas? Total in Dallas row is 450 and in sample is Probability a person is from Dallas is 450/1000=.45

9. What is the probability a person responded yes and is from Dallas? Categories intersect. The number in the intersecting cell is 150. Probability a person responded yes and is from Dallas is 150/1000=.15

10. What is the probability a person responded yes or is from Dallas? Categories are not mutually exclusive. There are 400 who responded yes and 450 from Dallas, however 150 of them are in both categories. Probability a person responded yes or is from Dallas is (.4)+ (.45)- (.15)=.7

11. What is the probability a person responded yes given they are from Dallas? Only refer to the Dallas column. Probability a person responded yes given they are from Dallas is 150/450=.33

12. What is the probability a person is from Dallas given they responded yes? Only refer to the Yes row. Probability a person is from Dallas given they responded yes is 150/400=.375

In the book Chances: Risk and Odds of every day life, James Burke says that 56% of the general population wears eyeglasses, while only 3.6% wears contacts. He also noted that of those who do wear glasses, 55.4% are women and 44.6% are men. Of those who wear contacts, 63.1% are women and 36.9% are men. Assume that no one wears both glasses and contacts. For the next person you encounter at random, what is the probability that this person is 13. A woman wearing glasses? 14. A man wearing glasses? 15. A woman wearing contacts? 16. A man wearing contacts? 17. None of the above?

First symbolize the given information: P(person wears glasses)= 56% P(woman, given wears glasses)= 55.4% P(man, given wears glasses)= 44.6% P(person wears contacts)= 3.6% P(woman, given wears contacts)= 63.1% P(man, given wears contacts)= 36.9% 13. A woman wearing glasses: P(wears glasses and woman) use multiplication rule: P(person wears glasses)P(woman, given wears glasses)= (56%)(55.4%)=.31 or 31%

First symbolize the given information: P(person wears glasses)= 56% P(woman, given wears glasses)= 55.4% P(man, given wears glasses)= 44.6% P(person wears contacts)= 3.6% P(woman, given wears contacts)= 63.1% P(man, given wears contacts)= 36.9% 14. A man wearing glasses: P(wears glasses and man) use multiplication rule: P(person wears glasses)P(man, given wears glasses)= (56%)(44.6%)=.25 or 25%

First symbolize the given information: P(person wears glasses)= 56% P(woman, given wears glasses)= 55.4% P(man, given wears glasses)= 44.6% P(person wears contacts)= 3.6% P(woman, given wears contacts)= 63.1% P(man, given wears contacts)= 36.9% 15. A woman wearing contacts: P(wears contacts and woman) use multiplication rule: P(person wears contacts)P(woman, given wears contacts)= (3.6%)(63.1%)=.023 or 2.3%

First symbolize the given information: P(person wears glasses)= 56% P(woman, given wears glasses)= 55.4% P(man, given wears glasses)= 44.6% P(person wears contacts)= 3.6% P(woman, given wears contacts)= 63.1% P(man, given wears contacts)= 36.9% 16. A man wearing contacts: P(wears contacts and man) use multiplication rule: P(person wears contacts)P(man, given wears contacts)= (3.6%)(36.9%)=.013 or 1.3%

First symbolize the given information: P(person wears glasses)= 56% P(woman, given wears glasses)= 55.4% P(man, given wears glasses)= 44.6% P(person wears contacts)= 3.6% P(woman, given wears contacts)= 63.1% P(man, given wears contacts)= 36.9% 17. Neither. First compute P(person wears contacts OR glasses) by adding the probabilities 56% and 3.6% (=59.6%). 59.6% of the population wears either glasses or contacts. Using the complement rule we can find the probability that the person does not wear either: 100% %= 40.4% (or in decimal form:1-.596=.404)

Wing Foot is a shoe franchise commonly found in shopping centers across the U.S. Wing Foot knows that its stores will not show a profit unless they make over $540,000 per year. Let A be the event that a new Wing Foot store makes over $540,000 its first year. Let B be the event that a store makes more than $540,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. The accounting office at Wing Foot provided the following information: 65% of all Wing Foot stores show a profit the first year; 71% of all Wing Foot stores show a profit the second year (this included stores that did not show a profit in the first year); however, 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute the following: a) P(A); b) P(B); c) P(B, given A); d) P(A and B); e) P(A or B) f) What is the probability that a new Wing Foot store will not be closed after 2 years? What is the probability that a new Wing Foot store will be closed after 2 years?

a) P(A)=.65 b) P(B)=.71 c) Since the problem states that 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year: P(B, given A)=.87 d) The events A and B are dependent [P(B)≠P(B|A)]. So P(A and B)= P(A)P(B|A) =(.65)(.87) =.5655

e) The events A and B are not mutually exclusive. There were stores successful in both years. So, P(A or B)= P(A)+ P(B)- P(A and B) = =.7945 f) The administrative policy is to close a store if it does not show a profit in either of the first two years. Therefore, there is a probability of 79.45% that a new Wing Foot store will not be closed after 2 years. There is a probability of ( =.2055) 20.55% that a new store will be closed after two years.