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5.1 – Practice and Exercises Name P1. Suppose Jack and Jill use a sample of four people who do not know the difference between tap water and bottle water. a. Construct the probability distribution for the number of people who would choose tap water. b. What is the probability that all four people will identify the tap water correctly? P3. Suppose you flip a coin and then roll a die. If you get heads and a 3, then your outcome is H3. a. List the sample space. b. Are the outcomes in your sample space equally likely? c. What is the probability that you get heads and a 3? P6. Suppose you pick four students at random from your school and check whether they are left-­‐
handed or right-­‐handed. a. Can you list a sample space? b. Can you determine the probability that all four students are right-­‐handed? E1. Suppose you flip a coin five times and count the number of heads. a. List all the possible outcomes. b. Make a table that gives the probability distribution for the number of heads. P8. Suppose you ask a person to taste a particular brand of strawberry ice cream and evaluate it as good, okay, or poor on flavor and as acceptable or unacceptable on price. a. Show all the possible outcomes on a tree diagram. b. How many possible outcomes are there? c. Are all the outcomes equally likely? E8. Business is slow at Downhill Research. Jack and Jill decide to investigate the probability that a penny they found will land heads up wen spun. a. Jack spins the penny 500 times and gets 227 heads. What is his estimate of the probability that a penny will land heads up when spun? b. Jill spins the penny 50 times. Would you expect Jack or Jill to have an estimate closer to the true probability of the penny landing heads up? Explain. c. Jack and Jill now flip the penny 10,000 times. There results are recorded in Display 5.10 (page 300 in textbook). Copy the table and fill in the missing percentages. Does this illustrate the Law of Large Numbers? Explain. E10. Tran has six shirts (blue, green, red, yellow, and two white – one long-­‐sleeved, one short-­‐
sleeved) and four pairs of pants (brown, black, blue, and gray). a. Use the Fundamental Principle of Counting to find the number of possible outfits Tran can wear. b. Show all the possible outfits in a two-­‐way table.
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