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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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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鈥檚 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鈥檛 feel addicted. Use a random number generator to produce random integers from to . Record the number of 鈥檚 in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of 鈥檚 was or less.
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 鈥攖丑别 and 鈥攁re 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 鈥�and 鈥� in words. Then find the probability of this event.
d. Explain why . Then use the general addition rule to compute .
Cell phonesThe Pew Research Center asked a random sample of adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.
Suppose we select one of the survey respondents at random. What鈥檚 the probability that:
a. The person is not age to and does not own an iPhone?
b. The person is age to or owns an iPhone?
Colorful disksA jar contains disks: each of four colors鈥攔ed, green, blue, and Page Number: yellow. Each set of disks of the same color is numbered from to . Suppose you draw one disk at random from the jar. Define events : get a red disk, and : get a disk with the number .
a. Make a two-way table that describes the sample space in terms of events and .
b. Find and .
c. Describe the event 鈥�and 鈥� in words. Then find the probability of this event.
d. Explain why Then use the general addition rule to compute
Four-sided dice A four-sided die is a pyramid whose four faces are labeled
with the numbers and(see image). Imagine rolling two fair, four-sided dice and
recording the number that is showing at the base of each pyramid. For instance, you would
record a if the die landed as shown in the figure.
a. Give a probability model for this chance process.
b. Define event A as getting a sum of . Find P(A).
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