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Chapter 4: Q2 (page 174)

New Jersey Pick 6 In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. Do calculations for winning this lottery involve permutations or combinations? Why?

Short Answer

Expert verified

The calculation for winning the lottery involves combinations, as the order of the numbers does not matter.

Step by step solution

01

Given information

Six different numbers from 1 to 49 are selected in any order.

The lottery is won if the selected numbers match the numbers drawn, and order does not matter.

02

Differentiate between combination and permutation

Combination: The formula of combination is applied if only a certain number of items are to be selected from a pool without replacementsuch that order does not matter.

Permutation: The formula of permutation is applied if a certain number of items are to be selected from a pool without replacementsuch that order matters.

03

Identification for the given problem

It is given that six numbers are selected from 1 to 49 in any order and are then matched with the numbers of the lottery ticket.

As the order does not matter, the calculations involve combinations.

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Most popular questions from this chapter

Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using a \(1 bill or a \)1 bill, college students were given either a \(1 bill or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Purchased Gum

Kept the Money

Students Given A \(1 bill

27

46

Students Given a \)1 bill

12

34

Denomination Effect

a. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.

c. What do the preceding results suggest?

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

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In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana: Use If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana?

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Defective Pacemakers Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from “Pacemaker and ICD Generator Malfunctions,” by Maisel et al., Journal of the American Medical Association, Vol. 295, No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

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26 girls.
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