5. On each of four days next week (Monday thru

Thursday), Earl will shoot six free throws. Assume that Earl's shots satisfy the assumptions

of Bernoulli trials with p = 0.37.

(a) Compute the probability that on any particular day Earl obtains exactly two successes. For future reference, if Earl obtains exactly two successes on any particular day, then we say that the event "Brad"

has occurred.

(b) Refer to part (a). Compute the probability

that: next week Brad will occur on Monday and Thursday and will not occur on

Tuesday and Wednesday. (Note: You are

being asked to compute one probability.)

16. On each of four days next week (Monday thru

Thursday), Dan will shoot five free throws. Assume that Dan's shots satisfy the assumptions

of Bernoulli trials with p = 0.74.

(a) Compute the probability that on any particular day Dan obtains exactly three successes. For future reference, if Dan obtains exactly three successes on any particular day, then we say that the event "Mel"

has occurred.

(b) Refer to part (a). Compute the probability that: next week Mel will occur exactly

once and that one occurrence will be on

Monday. (Note: You are being asked to

compute one probability.)

17. Alex and Bruce each perform 200 dichotomous

trials. A success is the desirable outcome; it requires more skill than does a failure. You are

given the following information.

? Each of the men achieves exactly 90 successes.

? Alex exhibited evidence of improving

skill over time; and Bruce exhibited evidence of declining skill over time.

21. A random sample of size n = 250 yields 80

successes. Calculate the 95% confidence interval for p.

22. A random sample of size n = 452 yields 113

successes. Calculate the 95% confidence interval for p.

23. George enjoys throwing horse shoes. Last week

he tossed 150 shoes and obtained 36 ringers.

(Ringers are good.) Next week he plans to

throw 250 shoes. Assume that George's tosses

satisfy the assumptions of Bernoulli trials.

(a) Calculate the point prediction of the number of ringers that George will obtain next

week.

(b) Calculate the 90% prediction interval for

the number of ringers George will obtain

next week.

(c) It turns out that next week George obtains

62 ringers. Given this information, comment on your answers in parts (a) and (b)

4. Calculation practice: General multiplication rule. In the 1980s in Canada, 52% of adult men smoked. It was estimated that male smokers had a lifetime probability of 17.2% of developing lung cancer, whereas a nonsmoker had a 1.3% chance of getting lung cancer during his life (Villeneuve and Mao 1994).8 a. What is the conditional probability of a Canadian man getting cancer, given that he smoked in the 1980s? b. Draw a probability tree to show the proba- bility of getting lung cancer conditional on smoking. c. Using the tree, calculate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. d. Using the general multiplication rule, cal- culate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. Did you get the same answer as in (c)? e. Using the general multiplication rule, calcu- late the probability that a Canadian man in the 1980s both did not smoke and never con- tracted lung cancer.Example # 26: In 2006, 86% of U.S. households had cable TV. Choose 3 households at random. Find the probability that a)None of the 3 households had cable TV b)All 3 households had cable TV c)At least 1 out of 3 households had cable TV Example # 27: A coin is tossed 3 times. Find the probability of getting at least I tail. Example # 28: A coin is tossed 5 times. Find the probability of getting at least 1 tail. Example # 29: A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least I person's infection will not improved. 14Section 4.3: The Multiplication Rules and Conditional Probability. Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring. When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such way that the probability is changed, the events are said to be dependent events. Example # 19: Determine whether these events are dependent or independent: a) Tossing a coin and drawing a card from a deck. b) Drawing a ball from an um, not replacing it, and then drawing a second ball. c) Drawing a ball from an um, replacing it, and then drawing a second ball. Multiplication Rule 1 When two events A and B are independent, the probability of both occurring is P(A and B) = P(A) . P(B) Example # 20: A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die. Example # 21: An urn contains 5 red balls and 3 white balls. A ball is selected and its color noted. Then it is replaced. A second ball is selected and its color noted. Find the probability of each of these. a) Selecting two red balls. b) Selecting two white balls. c) Selecting I red ball and then I white ball. 11The conditional probability of event B in relationship to an event A is the probability that event B occurs after event A has already occurred. Multiplication Rule 2 When two events A and B are dependent, the probability of both occurring is P(A and B) = P(A) . P(B| A) Example # 22: An urn contains 5 red balls and 3 white balls. A ball is selected without replacement. Then a second ball is selected. Find the probability of each of these. a) Selecting two red balls. b) Selecting two white balls. c) Selecting I red ball and then I white ball. Formula for Conditional Probability The probability that the second event B occurs given that the first event A has occurred can be found by the following formula: P(B) A)= = P(A and B) P(A) Example # 23: At a large university, the probability that a student takes calculus and is on the dean's list is 0.042. The probability that the student is on the dean's list is 0.21. Find the probability that the student is taking calculus, given that he or she is on the dean's list. 12