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Chapter 5: Q. 32 (page 326)
Tossing coins Imagine tossing a fair coin times.
a. Give a probability model for this chance process.
b. Define event B as getting more heads than tails. Find P(B).
(a) There are total probability outcomes in the probablity model
(b) The probabilty of getting more heads than tails is
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Crawl before you walk (At what age do babies learn to crawl? Does it take
longer to learn in the winter, when babies are often bundled in clothes that restrict their
movement? Perhaps there might even be an association between babies鈥� crawling age and
the average temperature during the month they first try to crawl (around months after
birth). Data were collected from parents who brought their babies to the University of
Denver Infant Study Center to participate in one of a number of studies. Parents reported
the birth month and the age at which their child was first able to creep or crawl a distance
of feet within one minute. Information was obtained on infants. Crawling age is given in weeks, and average temperature (in degrees Fahrenheit) is
given for the month that is months after the birth month.
a. Make an appropriate graph to display the relationship between average temperature and
average crawling age. Describe what you see.
Some computer output from a least-squares regression analysis of the data is shown.
b. What is the equation of the least-squares regression line that describes the relationship
between average temperature and average crawling age? Define any variables that you
use.
c. Interpret the slope of the regression line.
d. Can we conclude that warmer temperatures months after babies are born causes them
to crawl sooner? Justify your answer.
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. .
In a sample ofstudents, say they are vegetarians. Of the vegetarians, eat both fish and eggs, eat eggs but not fish, and eat neither. Choose one of the vegetarians at
random. What is the probability that the chosen student eats fish or eggs?
a.
b.
c.
d.
e.
Union and intersection Suppose C and D are two events such that P(C), P(D), and
P(C 鈭� D). Find P(C 鈭� D).
The security system in a house has two units that set off an alarm when motion is
detected. Neither one is entirely reliable, but one or both always go off when there is
motion anywhere in the house. Suppose that for motion in a certain location, the
probability that detector A goes off and detector B does not go off is , and the
probability that detector A does not go off is . What is the probability that detector
B goes off?
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