In an experiment, there are n independent trials. For each trial, there are thre
ID: 3349913 • Letter: I
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 0.20; the probability of outcome B is 0.10; and the probability of outcome C is 0.70. 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 two 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 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 C to "success" and outcomes A and B to "failure."
Yes. Assign outcome A to "success" and outcomes B and C to "failure."
What is the probability of success on each trial?
Explanation / Answer
a) Here as we are determining the probability of four outcomes of type A, five of type B, and one of type C, therefore there are three outcomes here possible for each of the trial and therefore binomial distribution cannot be used here, only multinomial distribution has to be used to obtain the required probability here. Therefore the required answer here would be given as:
No. A binomial probability model applies to only two outcomes per trial.
b) Now here we have to find the probability of four outcomes of type A and six outcomes that are not of type A, therefore there are only two outcomes here - either we get an A or we dont get an A.
Hence the binomial probability distribution could be used here.
Yes. Assign outcome A to "success" and outcomes B and C to "failure."
The probability of success on each trial here is computed as: P(A) = 0.2
Therefore 0.2 is the probability of success here.
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