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Count the number of fours in 6 dice rolls. Does this process describe a binomial random variable?

a) Yes
b) No

1 Answer

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Final answer:

Yes, counting the number of fours in 6 dice rolls does describe a binomial random variable because it meets the criteria of a fixed number of independent trials, two possible outcomes for each trial, and a constant probability of success.

Step-by-step explanation:

Counting the number of fours in 6 dice rolls does describe a binomial random variable. This is because the process meets all the requirements: there are a fixed number of trials (6 rolls), each trial has only two outcomes (rolling a four or not rolling a four), the probability of success (rolling a four) is the same for each trial (1/6), and each roll is independent of the others. Hence, if we let X represent the number of fours rolled, this would indeed serve as a binomial random variable with parameters n=6 (number of trials) and p=1/6 (probability of success on each trial).

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