In Problems 7–16, determine which of the following probability...

Question

In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.

A basketball player who makes 80% of her free throws is asked to shoot free throws until she misses. The number of free-throw attempts is recorded.

Accepted Answer

Welcome back, everyone. In this problem, a student answers a quiz containing exactly 12 independent multiple choice questions, each with 1 correct answer. The number of correct answers is recorded. Is this a binomial experiment? Select the best answer. A says yes, this is a binomial experiment because all the conditions are satisfied. B says no, this is not a binomial experiment because the probability of success is not 0.5. No, this is not a binomial experiment because the number of trials is not fixed. And D, yes, this is a binomial experiment because there are 4 possible outcomes. Now, in order to figure out if this really is a binomial experiment, let's first ask ourselves, what do we know about these types of experiments. Well, for starters, we know that there must be a fixed number of trials. We also know that there have there have to be two possible outcomes, hence the name binomial experiment. There must be a constant probability of success. OK. And we know that there must be independence, OK? So now we can ask ourselves, based on our problem statement, does this experiment fit all of these criteria? Well, for starters, we're told that the quiz contains exactly 12 multiple choice questions, so that means the number of trials is fixed, so it satisfies that criteria because it has exactly 12 2 trials or 12 questions, OK? Next, is there, does it have two possible outcomes? Yes, because each question, the result is either that it's incorrect or sorry that it's correct or that it is incorrect. How about if it has a constant probability of success? Well, the probability of success, the correct answer is constant for each child. And in our problem we're told that the quiz contains these 12 independent multiple choice questions, so independence is guaranteed. Therefore, since all the conditions for a binomial experiment are met, this scenario represents a binomial experiment. Let's look at our answer choices to see which is correct. A says yes, this is a binomial experiment because all the conditions are satisfied, so it is the correct answer. We can be sure by reviewing the remaining choices. In answer to SB, it says it isn't a binomial experiment because the probability of success is not 0.5, but the probability of success does not need to be 0.5 for a binomial experiment. It can be any constant value. In C, it says it's not a binomial experiment because the number of trials is not fixed, but we've already seen that the number of trials are fixed at 12, so this condition is satisfied. Indeed it says yes, this is a binomial experiment because there are 4 possible outcomes, but that's incorrect. There are 2 possible outcomes whether it's correct or not, not that there are 4 outcomes. So that's what we're sure that A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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