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 0.30; the probability of outcome B is 0.50; and the probability of outcome C is 0.20. Suppose there are 10 trials.

(1) 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.

a.Yes. A binomial probability model applies to three outcomes per trial.

b.No. A binomial probability model applies to only two outcomes per trial.

c.Yes. Each outcome has a probability of success and failure.

d.No. A binomial probability model applies to only one outcome per trial.

(2) 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.

a.Yes. Assign outcome C to "success" and outcomes A and B to "failure."

b.Yes. Assign outcome A to "success" and outcomes B and C to "failure."

c.Yes. Assign outcome B to "success" and outcomes A and C to "failure."

d.No. A binomial probability model applies to only two outcomes per trial.

(3)What is the probability of success on each trial?

The statement states that whether the probability of outcomes of type A, type B and type C can be calculated or not. We clearly sees that in this scenario the outcomes are greater than 2 on each trial, so the binomial model can't be applied.

So, option b is correct.

2.

The binomial model can be applied when there are two outcomes on each trial.

So, when the type A is discussed it would be either outcome A or not outcome A. The success would be occurrence of outcome A and failure would be not nonoccurence of outcome A. Thus, the binomial model is applicable. We can assign outcome A as a success in this scenario and outcomes B and C as failure.

So, option b is correct.

3.

The probability of success would be the probability of occurrence of outcome A. We are given that the probability of occurrence of outcome A is 0.3. So,

Probability of success on each trail=p=0.3