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Chapter 4: Q19 (page 143)
In Exercises 13鈥�20, express the indicated degree of likelihood as a probability value between 0 and 1.
Square Peg Sydney Smith wrote in 鈥淥n the Conduct of the Understanding鈥� that it is impossible to fit a square peg in a round hole.
The probability of fitting a square peg in a round hole is 0.
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If a month is randomly selected after mixing the pages from a calendar, what is the probability that it is a month containing the letter y?
ATM You want to obtain cash by using an ATM, but it鈥檚 dark and you can鈥檛 see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.
a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?
b. What is the probability of randomly selecting the card鈥檚 position and finding that it is incorrectly inserted on the first attempt, but it is correctly inserted on the second attempt? (Assume that the same position used for the first attempt could also be used for the second attempt.)
c. How many random selections are required to be absolutely sure that the card works because it is inserted correctly?
Composite Water Samples The Fairfield County Department of Public Health tests water for the presence of E. coli (Escherichia coli) bacteria. To reduce laboratory costs, water samples from 10 public swimming areas are combined for one test, and further testing is done only if the combined sample tests positive. Based on past results, there is a 0.005 probability of finding E. coli bacteria in a public swimming area. Find the probability that a combined sample from 10 public swimming areas will reveal the presence of E. coli bacteria. Is that probability low enough so that further testing of the individual samples is rarely necessary?
In Exercises 5鈥�36, express all probabilities as fractions.
Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 140th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinela bet if random horse selections are made?
Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births.
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