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Chapter 6: Problem 61

A die is rolled 5 times, and the number of spots for each roll is recorded. Explain why this is not a binomial experiment. Name a condition for use of the binomial model that is not met.

Short Answer

Expert verified
This is not a binomial experiment, because there are more than two possible outcomes on each roll of the die, and the probability of 'success' is not the same for each trial.

Step by step solution

01

Identify the outcomes of the experiment

For each roll of the die, the possible outcomes are 1, 2, 3, 4, 5, and 6. There are six possible outcomes for each roll, not just two.
02

Check if the outcomes are independent

The result of one roll of the die does not influence the result of any other roll. Therefore, the outcomes of each trial are independent. This condition for a binomial experiment is met.
03

Check if the probability of success is same for each trial

In order for an experiment to be considered a binomial experiment, there should be a fixed number of trials with two possible outcomes for each trial: a 'success' and a 'failure'. And the probability of success should be the same for each trial. But in this experiment, there are six possible outcomes for each roll with the probability of each outcome being different(1/6), and not same for each trial.

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