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 0.20; the probability of outcome B is 0.30; and the probability of outcome C is 0.50. 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.
No. A binomial probability model applies to only two outcomes per trial.
Yes. A binomial probability model applies to three outcomes per trial.
Yes. Each outcome has a probability of success and failure.
No. A binomial probability model applies to only one outcome per trial.
(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.
Yes. Assign outcome C to "success" and outcomes A and B to "failure."
Yes. Assign outcome B to "success" and outcomes A and C to "failure."
No. A binomial probability model applies to only two outcomes per trial.
Yes. Assign outcome A to "success" and outcomes B and C to "failure."
What is the probability of success on each trial?
a) A binomial probability can only be computed where each trial has two outcomes, here we got three outcomes A, B and C and therefore this is not a binomial distribution but a multinomial distribution here.
Therefore No binomial probability model cannot be applied here as binomial model only applies to two outcomes per trial.
Therefore A is the correct answer here.
b) Yes we can apply the binomial model here, as there are only two outcomes for each trial in this case: A or not A.
Therefore the success here would be given as: A as the outcome.
Therefore D is the correct answer here that is Yes. Assign outcome A to "success" and outcomes B and C to "failure."
The probability of success here is the probability of outcome A that is 0.2 here
Therefore the probability of success in each trial here is 0.2
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