Question

Determine whether the given random variable has a binomial distribution. Justify your answer. Put the names of all the students in your class in a hat. Mix them up, and draw four names without looking. Let Y = the number whose last names have more than six letters.

Answer 1

No, it does not

Explanation:

The binomial distribution is used when the variable has only two possible outcomes, and each trial is independent of each other.

In this question:

For each student, yes, there are only two possible outcomes. Either their last names have more than six letters, or it does not.

However, as you pick, the names are not returned to the hat, so the probabilities change, which means that the trials are not independent, and we do not have a binomial distribution.