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

Isa Trevino

Isa Trevino

Answered question

2021-09-15

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 0.80; the probability of outcome B is 0.10; and the probability of outcome C is 0.10. 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. Each outcome has a probability of success and failure.
b) No. A binomial probability model applies to only two outcomes per trial.
c) Yes. A binomial probability model applies to three outcomes per trial.
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 B to "success" and outcomes A and C to "failure."
b) No. A binomial probability model applies to only two outcomes per trial.
c) Yes. Assign outcome C to "success" and outcomes A and B to "failure."
d) Yes. Assign outcome A to "success" and outcomes B and C to "failure."
What is the probability of success on each trial?

Answer & Explanation

estenutC

estenutC

Skilled2021-09-16Added 81 answers

Step 1
In the case of binomial experiment, each trial have only two possible outcomes. Here in the question, we have more than two outcomes i.e. 3 outcomes.
a) Answer:
Option B is correct. i.e.
No. A binomial probability model applies to only two outcomes per trial
b) Answer:
Option D is correct, i.e.
Yes. Assign outcome A to "success" and outcomes B and C to "failure."
Step 2
Probability of success on each trial is given by
Applying Binomial theorem
Probability of x success out of n trial is given by
P(X=x)=(beg{array}{c}nxend{array})×px×(1p)nx
P(X=4)=(beg{array}{c}104end{array})×0.804×(10.80)104
=10!4!×(104)!×0.804×(10.80)104
=0.005505
Step 3
Answer:
Probability of success on each trial is 0.005505

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