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Chapter 5: Q. 58 (page 329)
If a player rolls a , it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?
a.
b.
c.
d.
e.
The probability of getting craps or an even sum on one roll of the dice is (d)
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Mystery box Ms. Tyson keeps a Mystery Box in her classroom. If a student meets expectations for behavior, she or he is allowed to draw a slip of paper without looking. The slips are all of equal size, are well mixed, and have the name of a prize written on them. One of the 鈥減rizes鈥濃�攅xtra homework鈥攊sn鈥檛 very desirable! Here is the probability model for the prizes a student can win:
a. Explain why this is a valid probability model.
b. Find the probability that a student does not win extra homework.
c. What鈥檚 the probability that a student wins candy or a homework pass?
Random assignment Researchers recruited volunteers-men and women-to take part in an experiment. They randomly assigned the subjects into two groups of people each. To their surprise, of the men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in or more of the men ending up in the same group.
Get identical slips of paper. Write "" on of the slips and "" on the remaining slips. Put the slips into a hat and mix well. Draw of the slips without looking and place into one pile representing Group . Place the other slips in a pile representing Group . Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which or more men ended up in the same group.
Another commercial If Aaron tunes into his favorite radio station at a
randomly selected time, there is a probability that a commercial will be playing.
a. Interpret this probability as a long-run relative frequency.
b. If Aaron tunes into this station at randomly selected times, will there be exactly one
time when a commercial is playing? Explain your answer.
Taking the train According to New Jersey Transit, the weekday train from Princeton to New York City has a chance of arriving on time. To test this claim, an auditor chooses weekdays at random during a month to ride this train. The train arrives late on of those days. Does the auditor have convincing evidence that the company's claim is false? Describe how you would carry out a simulation to estimate the probability that a train with a chance of arriving on time each day would be late on or more of days. Do not perform the simulation.
Does the new hire use drugs? Many employers require prospective employees to
take a drug test. A positive result on this test suggests that the prospective employee uses
illegal drugs. However, not all people who test positive use illegal drugs. The test result
could be a false positive. A negative test result could be a false negative if the person
really does use illegal drugs. Suppose that of prospective employees use drugs and
that the drug test has a false positive rate of and a false negative rate of.
Imagine choosing a prospective employee at random.
a. Draw a tree diagram to model this chance process.
b. Find the probability that the drug test result is positive.
c. If the prospective employee鈥檚 drug test result is positive, find the probability that she
or he uses illegal drugs.
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