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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 5 - Discrete Probability DistributionsProblem 5.CRE.2b
Chapter 5, Problem 5.CRE.2b

Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.


b. If you play this game once every day, find the mean number of wins in years with exactly 365 days.

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1
Step 1: Understand the problem. The Kentucky Pick 4 lottery involves selecting four digits with repetition allowed, meaning each digit can range from 0 to 9. The total number of possible combinations is calculated as 10^4, since there are 10 choices for each of the 4 digits.
Step 2: Calculate the probability of winning. Since there is only one winning combination out of the total possible combinations, the probability of winning on a single ticket is given by P(win) = 1 / (10^4).
Step 3: Determine the number of days played in a year. The problem states that the game is played once every day in a year with 365 days. Therefore, the total number of games played in a year is 365.
Step 4: Use the formula for the mean number of wins. The mean number of wins in a given number of trials is calculated as μ = n * P(win), where n is the number of trials (365 days) and P(win) is the probability of winning on a single ticket.
Step 5: Substitute the values into the formula. Replace n with 365 and P(win) with 1 / (10^4) to compute the mean number of wins. The result will represent the expected number of wins in a year with 365 days.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of the Kentucky Pick 4 lottery, the probability of winning with a single ticket can be calculated based on the total number of possible combinations of four digits, considering that repetition is allowed.
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Expected Value

Expected value is a statistical concept that provides a measure of the center of a probability distribution, representing the average outcome if an experiment is repeated many times. In this lottery scenario, the expected number of wins over a year can be calculated by multiplying the probability of winning by the number of plays (365 days).
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Mean

The mean, or average, is a fundamental statistical measure that summarizes a set of values by dividing the sum of those values by the number of values. In this case, the mean number of wins in a year can be derived from the expected value, indicating how many times a player can expect to win if they play the lottery daily.
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Related Practice
Textbook Question

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.


0 0 1 2 17 28 21 8


c. Find the mode.

d. Find the range.

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Textbook Question

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Textbook Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



c. If two different challenges are randomly selected without replacement, find the probability that they both resulted in an overturned call.

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Textbook Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



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Textbook Question

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.


0 0 1 2 17 28 21 8


i. What is the level of measurement of the data: nominal, ordinal, interval, or ratio?

j. Are the data discrete or continuous?

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Textbook Question

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.


0 0 1 2 17 28 21 8


a. Find the mean.

b. Find the median.

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