### All Common Core: High School - Statistics and Probability Resources

## Example Questions

### Example Question #1 : Probability Concepts To Analyze Decisions And Strategies: Ccss.Math.Content.Hss Md.B.7

Calculate the probability that a stock return, R, is either below -7% or above 7%. Are these two events mutually exclusive?

**Possible Answers:**

.07, no

.0345, yes

.38, yes

.38, no

Cannot be determined because the two events are not mutually exclusive.

**Correct answer:**

.38, yes

### Example Question #86 : Using Probability To Make Decisions

Cataclysmic storms possess the following fatality rate:

A town with a population of is hit with a tornado that decimates the town. Would it be fair to say that only one person will be fatally injured in the storm?

**Possible Answers:**

No, statistics are guides not absolute predictions

Yes, statistics are absolute predictions not guides

No, statistics are absolute predictions not guides

Yes, statistics are guides not absolute predictions

Cannot be determined

**Correct answer:**

No, statistics are guides not absolute predictions

This standard asks us to analyze decisions and strategies using probability concepts (e.g. product testing and medical testing). Questions associated with these standards ask us to not simply calculate probabilities and statistics but to also understand the logic associated with them. In other words, simply understanding the mathematics behind probability operations does not always equate to real-world problem solving abilities.

In a similar vein, this standard attempts to point out that the base memorization of equations is irrelevant; rather, you are required to focus on understanding the logic behind these questions and applying this knowledge to the analysis of real-world situations. As you study this standard, it is important to note that understanding the logic behind statistics may decrease the difficulty of other problems; thus, you should be able to not only choose a correct answer but also be able to explain the reasoning behind it. In this way we understand that these problems can be solved by plugging variables into formulae to solve equations; however, we aim to understand why the variables interact with one another in a predictable manner.

Lets's solve the problem. The problem states that the probability of being fatally injured in a cataclysmic storm is the following:

In the problem a town is struck by a cataclysmic tornado. The town coincidentally has the following population:

Does this mean that only one person is likely to die in the storm. The correct answer is "no, statistics are guides not absolute predictions." There are far too many factors to be considered in this scenario. According to previous samples and statistics, we have calculated what could be an accurate probability of fatal injury in a cataclysmic storm; however, it is a prediction. No statistic is absolute because there are an infinite number of ways that events can occur and it is impossible for us to sample them all. If we could perform this calculation on an infinite number of occurrences and create a population parameter of every storm in the history of the earth, then we could make this prediction with more certainty. The fact of the matter is that probabilities are a guide, we can assume that in this event one person is likely to be injured; however, depending on circumstances (such as the availability of shelters and efficacy of storm notifications) less or more people may be injured. It would be a fallacy to say that only a single person could be fatally injured in the storm. Now, if we said that one out of ten people win a prize in a drawing, then we can say one person will definitely win because that is a rule of the game and a constituent component of the way it is constructed and played. This is not the same as a natural event such as a crash, storm, or bolt of lightening.