General: Combination Lock To open a combination lock, you

Statistical Literacy Consider the following two events for an individual: A  owns a cell phone B  owns a laptop computer Translate each event into words. (a) Ac (d) A  B (b) A and B (e) B  A (c) A or B

Critical Thinking You are given the information that P(A)  0.30 and P(B)  0.40. (a) Do you have enough information to compute P(A or B)? Explain. (b) If you know that events A and B are mutually exclusive, do you have enough information to compute P(A or B)? Explain.

Critical Thinking You are given the information that P(A)  0.30 and P(B)  0.40. (a) Do you have enough information to compute P(A and B)? Explain. (b) If you know that events A and B are independent, do you have enough information to compute P(A and B)? Explain.

Critical Thinking For a class activity, your group has been assigned the task of generating a quiz question that requires use of the formula for conditional probability to compute P(B  A). Your group comes up with the following question: If P(A and B)  0.40 and P(A)  0.20, what is the value of P(B  A)? What is wrong with this question? Hint: Consider the answer you get when using the correct formula, P(B | A)  P(A and B) / P(A).

Salary Raise: Women Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one (USA Today). According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities: P(woman asked for a raise); P(woman received raise, given she asked for one); P(woman asked for raise and received raise).

Salary Raise: Men According to the same survey quoted in Problem 5, of the men interviewed, 20% had asked for a raise and 59% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities: P(man asked for a raise); P(man received raise, given he asked for one); P(man asked for raise and received raise).

General: Thumbtack Drop a thumbtack and observe how it lands. (a) Describe how you could use a relative frequency to estimate the probability that a thumbtack will land with its flat side down. (b) What is the sample space of outcomes for the thumbtack? (c) How would you make a probability assignment to this sample space if, when you drop 500 tacks, 340 land flat side down?

Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in Table 4-5. Lets use the following notation for the various events: W  washing oil off within 5 minutes, A  washing oil off after 5 minutes, N  no reaction, M  mild reaction, S  strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (a) P(N), P(M), P(S) (b) P(N  W), P(S  W) (c) P(N  A), P(S  A) (d) P(N and W), P(M and W) (e) P(N or M). Are the events N  no reaction and M  mild reaction mutually exclusive? Explain. (f) Are the events N  no reaction and W  washing oil off within 5 minutes independent? Explain.

General: Two Dice In a game of craps, you roll two fair dice. Whether you win or lose depends on the sum of the numbers occurring on the tops of the dice. Let x be the random variable that represents the sum of the numbers on the tops of the dice. (a) What values can x take on? (b) What is the probability distribution of these x values (that is, what is the probability that x  2, 3, etc.)?

Academic: Passing French Class records at Rockwood College indicate that a student selected at random has probability 0.77 of passing French 101. For the student who passes French 101, the probability is 0.90 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102?

Combination: City Council There is money to send two of eight city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of two council members can be selected from the eight who want to go to the conference?

Compute. (a) P7,2 (b) C7,2 (c) P3,3 (d) C4,4

Counting: Exam Answers There are five multiple-choice questions on an exam, each with four possible answers. Determine the number of possible answer sequences for the five questions. Only one of the sets can contain all five correct answers. If you are guessing, so that you are as likely to choose one sequence of answers as another, what is the probability of getting all five answers correct?

Scheduling: College Courses A student must satisfy the literature, social science, and philosophy requirements this semester. There are four literature courses to select from, three social science courses, and two philosophy courses. Make a tree diagram showing all the possible sequences of literature, social science, and philosophy courses.

General: Combination Lock To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 10 numbers, 0 through 9, determine the number of different combinations possible for the lock. (Note: The same number can be reused.)

General: Combination Lock You have a combination lock. Again, to open it you turn the dial to the right and stop at a first number; then you turn it to the left and stop at a second number. Finally, you turn the dial to the right and stop at a third number. Suppose you remember that the three numbers for your lock are 2, 9, and 5, but you dont remember the order in which the numbers occur. How many sequences of these three numbers are possible?