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Chapter 5: Problem 51

Which of the following are binomial experiments? Explain why. a. Rolling a die many times and observing the number of spots b. Rolling a die many times and observing whether the number obtained is even or odd c. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when \(54 \%\) of all voters are known to be in favor of this proposition.

Short Answer

Expert verified
Scenario B and Scenario C are binomial experiments because they meet the required criteria: a series of identical trials, two possible outcomes (success or failure) with constant probabilities, and independent trials.

Step by step solution

01

Examine Scenario A

We're rolling a die many times and observing the number of spots. This isn't a binomial experiment because the outcome isn't simply a success or failure - it can result in six possible outcomes.
02

Examine Scenario B

We're rolling a die many times and observing whether the number obtained is even or odd. This IS a binomial experiment because there are only two outcomes - success (obtaining an even number) or failure (obtaining an odd number). The probability of each remains constant (0.5), and each roll of the die is an independent event.
03

Examine Scenario C

We're selecting a few voters from a large population and observing whether or not each favors a certain proposition. This IS a binomial experiment because there are only two outcomes - success (voter is in favor of the proposition) or failure (voter isn't in favor). The probability for each outcome (0.54 for success, 0.46 for failure) remains constant for the population, and the selection of one voter does not influence the selection of another.

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Most popular questions from this chapter

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