In an experiment, there are n independent trials. For each trial, there are thre

Question

In an experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.70; the probability of outcome B is 0.20; and the probability of outcome C is 0.10. Suppose there are 10 trials. (a) Can we use the binomial experiment model to determine the probability of four outcomes of type A, five of type B, and one of type C? Explain. Yes. A binomial probability model applies to three outcomes per trial. No. A binomial probability model applies to only one outcome per trial. No. A binomial probability model applies to only two outcomes per trial Yes. Each outcome has a probability of success and failure. (b) Can we use the binomial experiment model to determine the probability of four outcomes of type A and six outcomes that are not of type A? Explain. O No. A binomial probability model applies to only two outcomes per trial Yes. Assign outcome C to·success" and outcomes A and 8 to-failure." Yes. Assign outcome A to "success" and outcomes B and C to failure." Yes. Assign outcome B to "success" and outcomes A and C to "failure." What is the probability of success on each trial? O Type here to search 3//2018

Explanation / Answer

(a) Option 3 is correct. No. A binomial probability model applies to only two outcomes per trial.

In this experiment, every trial can have three outcomes. Hence, a binomial probability model which has only two possible outcomes (normally called success and failure) per trial cannot be applied.

Option 1 and 2 are incorrect as a binomial probability model applies to exactly two outcomes per trial,

Option 4 is incorrect because it is a general statement and is not relevant to what the question is about.

(b) Option 3 is correct. Yes. Assign outcome A to success and outcome B and C to failure.

Now, we are converting the problem to each trial having an outcome of A or not-A, i.e. B or C. Normally, in a binomial probability model, there are exactly two outcomes typically called success and failure. So, to use this model, we can map A to success and B or C to failure and apply it to the model.

Option 1 is incorrect, as the correct answer is yes.

Option 2 and 4 are incorrect answers as just mapping C or B to success does not give use the required probabilities.

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