Question

A binomial model shows that two outcomes have the same probability of occurring. In an experiment with 60 trials to test this model, the researcher found that Outcome A occurred 36 times. How did the experimental outcome compare to the theoretical model? A. The result for Outcome A was 6 more than expected. B. Outcome B occurred 36% of the time rather than the expected 50%. C. The result for Outcome B was 4 less than expected. D. Outcome A had an expected probability of 50% but an actual probability of 36%. Please explain how to get the answer!

Answer 1

the result for Outcome A was 6 more than expected (A)

Explanation:

Given:

The binomial model has two outcomes that have the same probability of occurring.

n= number of trials = 60 trials

After the experiment, the researcher found that Outcome A occurred 36 times. This implies the experimental probability of outcome A = 36times

In a binomial distribution, there is a fixed number of trials = n.

There are only two possible outcome in a trial: a success and a failure.

When n= 1

Let p = the probability of a success = 0.5

q = the probability of a failure = 0.5

The sum of the probability of a success and failure = 1

p + q = 0.5+0.5 = 1

The theoretical probability is what you expect to happen, but it isn't always what actually happens when the experiment is carried out

The theoretical probability of success for 1 trial = The theoretical probability of failure for 1 trial= 0.5

when n = 60trials

The theoretical probability of outcome A = The theoretical probability of outcome B = 1/2 (60) = 30times

But the experimental probability of outcome A = 36times

This means that the experimental outcome of A = 6 more than the theoretical probability of outcome A

36 = 30 + 6

Therefore, the result for Outcome A was 6 more than expected (A)