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Chapter 4: Problem 40

Suppose you have a loaded die and you want to find the (approximate) probabilities of different outcomes for this die. How would you find these probabilities? What procedure would you use? Explain briefly.

Short Answer

Expert verified
To find the approximate probabilities for a loaded die, one would need to roll the die multiple times, recording the outcomes of each roll. The probabilities could then be calculated as the frequency of each outcome divided by the total number of trials. The probabilities should add up to approximately 1.

Step by step solution

01

Understand the nature of the die

Understand that a loaded die does not have equal probability for all its outcomes. Each face of the die is biased differently.
02

Perform an Experiment

Roll the die multiple times to perform an experiment. The more times the die is rolled, the more accurate the probabilities would be. Commonly, the experiment is carried out 100 or 1000 times to get more dependable results.
03

Record the Outcomes

Record the outcomes of each roll, making a count of how many times each outcome (face showing up) happens.
04

Calculate the Probability

The probability of a given outcome is calculated by counting the number of times that outcome occurred during the experiment, and dividing it by the total number of trials. Repeat this for each outcome in order to find the probabilities for all outcomes. In other words, if the face 'n' showed up 'a' times in 't' trials, the probability \(P(n)\) is given by, \(P(n) = \frac{a}{t}\).
05

Check the Probabilities

The calculated probabilities should add up to approximately 1. If they do not, then an error was made in the experiment or in the calculation.

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Most popular questions from this chapter

According to the U.S. Census Bureau's most recent data on the marital status of the 238 million Americans aged 15 years and older, \(123.7\) million are currently married and \(71.5\) million have never been married. If one person from these 238 million persons is selected at random, find the probability that this person is currently married or has never been married. Explain why this probability is not equal to \(1.0\).

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Given that \(A, B\), and \(C\) are three independent events, find their joint probability for the following. a. \(P(A)=.20, \quad P(B)=.46\), and \(P(C)=.25\) b. \(P(A)=.44, \quad P(B)=.27\), and \(P(C)=.43\)
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