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Chapter 5: Q. 47 (page 328)
Dogs and cats In one large city, of all households own a dog, own a cat, and own both. Suppose we randomly select a household. What鈥檚 the probability that the household owns a dog or a cat?
The likelihood that the household owns either a dog or a cat is
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You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is approximately . This means that
a. in every bridge deals, each player has ace exactly times.
b. in million bridge deals, the number of deals on which each player has ace will be exactly .
c. in a very large number of bridge deals, the percent of deals on which each player has ace will be very close to .
d. in a very large number of bridge deals, the average number of aces in a hand will be very close to .
e. If each player gets an ace in only of the first deals, then each player should get an ace in more than of the next deals.
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?
Union and intersection Suppose A and B are two events such that P (A), P (B), and
P (A鈭狟). Find P (A鈭〣).
When did you leave? The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle. Choose a trip at random and record the time at which the trip started. Here is an assignment of probabilities for the outcomes :
a. What probability should replace 鈥�?鈥� in the table? Why?
b. Find the probability that the chosen trip did not begin between A.M. and P.M.
Scrabble In the game of Scrabble, each player begins by randomly selecting tiles from a bag containing tiles. There are vowels, consonants, and blank tiles in the bag. Cait chooses her tiles and is surprised to discover that all of them are vowels. We want to perform a simulation to determine the probability that a player will randomly select vowels.
a. Describe how you would use a table of random digits to carry out this simulation.
b. Perform one trial of the simulation using the random digits given. Copy the digits onto your paper and mark directly on or above them so that someone can follow what you did.
c. In of the trials of the simulation, all tiles were vowels. Does this result give convincing evidence that the bag of tiles was not well mixed?
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