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Chapter 5: Q. T5.8 (page 357)
In a class, there are girls and boys. If the teacher selects two students at random
to attend a party with the principal, what is the probability that the two students are the
same sex?
The correct option is:
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Foreign-language studyChoose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:
a. What鈥檚 the probability that the student is studying a language other than English?
b. What is the probability that a student is studying Spanish given that he or she is
studying some language other than English?
Three machines鈥擜, B, and C鈥攁re used to produce a large quantity of identical parts at
a factory. Machine A produces of the parts, while Machines B and C produce
and of the parts, respectively. Historical records indicate that of the parts
produced by Machine A are defective, compared with for Machine B, and for
Machine C. Suppose we randomly select a part produced at the factory.
a. Find the probability that the part is defective.
b. If the part is inspected and found to be defective, what鈥檚 the probability that it was
produced by Machine B?
Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits鈥攃lubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as 鈥渇ace cards.鈥� Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.
| Type of card | |||
| Face card | Non-Face card | Total | |
| Heart | |||
| Non-Heart | |||
| Total | |||
Are the events 鈥渉eart鈥� and 鈥渇ace card鈥� independent? Justify your answer.
Waiting to park Do drivers take longer to leave their parking spaces when
someone is waiting? Researchers hung out in a parking lot and collected some data. The
graphs and numerical summaries display information about how long it took drivers to
exit their spaces.
a. Write a few sentences comparing these distributions.
b. Can we conclude that having someone waiting causes drivers to leave their spaces more
slowly? Why or why not?
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.
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