7B Preview

Preparing for the next class

In the next in-class activity, you will need to understand how to calculate theoretical  probabilities involving the words AND, OR, and NOT.

Question 1

In May 2021, SurveyUSA [1] interviewed 750 California adults and asked a number of  questions related to voting. One of the questions asked was:

“Are you registered to vote in California?”

SurveyUSA reported the following survey results.

Are you registered to  vote in California? Yes 645
No 98
Not Sure 7
Total 750
  1. What is the probability that a randomly selected California adult is registered  to vote? Round to the nearest hundredth.
  2. What is the probability that a randomly selected California adult is not  registered to vote? Round to the nearest hundredth.
  3. What is the probability that a randomly selected California adult is not sure if  they are registered to vote? Round to the nearest thousandth.
  4. Rounding to the nearest whole number, what is the sum of the probabilities you computed in Parts A through C?

Question 2

The same survey also asked the 750 respondents to identify their age group from  one of the following groups:

18-34, 35-49, 50-64, 65+

  1. The following are the frequencies for each age group. Fill in the missing  value in the table.
    What age group do you belong to?

    18–34 35–49 50–64 65+ Total
    233 195 180 750
  2. What is the probability that a randomly selected California adult is 65 years  old or older? Round to the nearest hundredth.
  3. What is the probability that a randomly selected California adult is less than  65 years old? Round to the nearest hundredth.
  4. What is the relationship between the probabilities calculated in Parts B and  C?  Hint: Think about their sum.

The event that a California adult is less than 65 years old can be written as the event  “NOT 65+.”

These two events, 65+ and NOT 65+, are referred to as complements because the  sum of their probabilities is equal to 1.

More generally, for any event A, we can think of the probability of complements as  having the following relationship:

[latex]P(A) + P(NOT A) = 1[/latex]

The equation can be rewritten as follows:

[latex]P(NOT A) = 1 - P(A)[/latex]

This tells us that for event A, the probability that the event will not occur is equal to 1  minus the probability that the event will occur.

Question 3

What is the complement of the event “18–34?”

Hint: Use the plus symbol like it is used in 65+.

Question 4

Suppose we want to investigate the answers to both questions in the survey in the  same table as follows:

What age group do you belong to?

18–34 35–49 50–64 65+ Total
Are you registered  to vote in

California?

 Yes 180 175 151 139 645
No 49 20 27 3 98
Not Sure 4 0 2 0 7
Total 233 195 180 142 750
  1. What is the probability that a randomly selected adult from California is  registered to vote? Notice where you found the counts used in your  calculations on the table. Round to the nearest hundredth.
  2. What is the probability that a randomly selected adult from California is 65+?  Notice where you found the counts used in your calculations on the table.  Round to the nearest hundredth.

    There are times when you want to combine two events with using the word AND or  the word OR.

    As an example, you may want to find the probability of it raining OR snowing on a  given day so that you can dress accordingly.

    In probability, AND means that both events must happen, and OR means one event,  the other event, or both events must happen.

  3. What is the probability that a randomly selected adult from California is 65+  AND registered to vote? Round to the nearest hundredth.

    When it is impossible for two events to happen at the same time, they are called  mutually-exclusive events. If A and B are mutually-exclusive events, then:

    [latex]P(A AND B) = 0[/latex]

    and

    [latex]P(A or B) = P(A) + P(B)[/latex]

  4.  What is the probability that a randomly selected adult from California is 18– 34 AND 35–49? Round to the nearest hundredth.

    Hint: Is it possible to be in two age groups?

  5. What is the probability that a randomly selected adult from California is 18– 34 OR 35–49? Round to the nearest hundredth.

    Hint: Are “18–34” and “35–49” mutually-exclusive events? If so, use the formula.

 

 

 

  1. SurveyUSA. (2021, May 3). Results of SurveyUSA News Poll #25925. https://www.surveyusa.com/client/PollReport.aspx?g=e3ae1d7e-9d6e-44b2-b1f8-e51c51df9ea2 ↵