Question

Often times there are so many variables involved in a study that it is difficult to distinguish "causes". For example, there is the belief that "smoking causes lung cancer". I tend to believe this myself but my own mother was a chain smoker and never developed lung cancer. There are many other variables that might affect the outcome of lung cancer such as working conditions, heredity, diet, etc.

It is too hard to account for every "factor" in these circumstances so we might just focus on one such as studying lung cancer patients and asking them if they smoked or not.

In this discussion, you are going to come up with some examples of the binomial probability distribution. Remember our definition:Def: Binomial probability distribution
1. procedure has fixed # of trials
2. trials must be independent
3. each trial must have all outcomes classified into 2 categories
4. probabilities must remain constant for each trial

For example, we interview 50 lung cancer patients (fixed # of trials). They come from all occupations and parts of the state (independence). Either they smoked or did not smoke (2 categories). If 15% of the population smokes then the probability would remain constant for each trial equaling 15% or 0.15. This would meet the conditions for a binomial probability distribution.

give examples of a binomial probability distribution. It can be made up, you do not need actual numbers.

Answer 1

Solution: The binomial probability distribution is:

Suppose it is known that in a particular country about 12% of its adult population has been to Paris. Now if we randomly select 10 adults from this population and ask them if they have been to Paris.

The random variable say, x denotes the number of adults who will say that they have been to Paris follows the Binomial probability distribution with n = 10 and p = 0.12 because the random variable follows the below conditions:

1. The given random experiment has a fixed number of trials as we have 10 adults under consideration.

2. The answer to the given question for each adult is independent of the other adult.

3. Each trial has two possible outcomes like either he/she has been to Paris or he/she has not been to Paris

4. The probability of an adult has been to Paris is constant 0.12 for all the trails.