Chapter 5: Q. 24 (page 312)
If I toss a fair coin five times and the outcomes are , then the probability that tails appear on the next toss is
a. .
b. less than .
c. greater than .
d. .
e. .
The correct option is (a) i.e.
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Checking independence Suppose C and D are two events such that
and Are events C and D independent? Justify your answer.
Roulette An American roulette wheel has 38 slots with numbers throughand , as shown in the figure. Of the numbered slots, are red, are black, and —the and —are green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events : ball lands in a black slot, and : ball lands in an even-numbered slot. (Treatand as even numbers.)
a. Make a two-way table that displays the sample space in terms of events and .
b. Find and.
c. Describe the event “and ” in words. Then find the probability of this event.
d. Explain why . Then use the general addition rule to compute .
Dogs and cats In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household.
a. Make a Venn diagram to display the outcomes of this chance process using events D: owns a dog, and C: owns a cat.
b. Find P.
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.
Smartphone addiction? A media report claims that of U.S. teens with smartphones feel addicted to their devices. A skeptical researcher believes that this figure is too high. She decides to test the claim by taking a random sample of U.S. teens who have smartphones. Only of the teens in the sample feel addicted to their devices. Does this result give convincing evidence that the media report’s claim is too high? To find out, we want to perform a simulation to estimate the probability of getting or fewer teens who feel addicted to their devices in a random sample of size from a very large population of teens with smartphones in which 50% feel addicted to their devices.
Let = feels addicted and = doesn’t feel addicted. Use a random number generator to produce random integers from to . Record the number of ’s in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of ’s was or less.
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