Question

You randomly sample 5 people in your​ school, and none of them is a vegetarian. Does this mean that the probability of being a vegetarian for students at your school equals​ 0? Explain. Choose the correct answer below. A. Yes. Since no vegetarians were found during the​ survey, the probability is 0. If at a later point students who are vegetarian are​ found, this will increase the probability. B. No. In the short​ run, the proportion of a given outcome can fluctuate a lot. As more people are​ sampled, the proportion should approach the real probability. C. No. Probability is​ subjective, so if you​ (the surveyor) decide the probability should be greater than​ 0, then you can make it that way.

Answer 1

B.

Explanation:

The sample size taken for the school is too small.

5 people not being vegetarian does not mean NO OTHER students are vegetarian also. Thus, an assumption based on this probability of 5 people would not be correct unless fully supported. This makes option A wrong.

Answer B is correct because with small numbers, probability varies a lot and may change drastically with the addition of data.

For example: the 6th person we sample says he/she is a vegetarian.

This would change the probability drastically to 1/6 = 0.1667

Because this is a drastic change, and fluctuation is clear, answer B is correct.

C is wrong because probability is not subjective.