Conditional Probability & the Rules of Probability

Practice Questions

Common Core: High School - Statistics and Probability › Conditional Probability & the Rules of Probability

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1

Given the following data, what is the probability that a car will have a V8 or a manual transmission?

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2

Given the following data, what is the probability that a car will have a V8 or a manual transmission?

3

Given the following data, what is the probability that a car will have a V8 or a manual transmission?

4

A car dealership takes its automotive inventory. They decide to note the number of cars and trucks are in the lot as well as the type of transmission the vehicles have: automatic or manual. They input this data into the following table:

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A potential car buyer wants to purchase a vehicle and inquires if vehicle type is independent of transmission style. According to the data, is purchasing a truck independent of it possessing a manual transmission?

5

Given the following data, what is the probability that a car will have a V8 or a manual transmission?

6

A car dealership takes its automotive inventory. They decide to note the number of cars and trucks are in the lot as well as the type of transmission the vehicles have: automatic or manual. They input this data into the following table:

Screen shot 2016 03 08 at 2.37.54 pm

A potential car buyer wants to purchase a vehicle and inquires if vehicle type is independent of transmission style. According to the data, is purchasing a truck independent of it possessing a manual transmission?

7

Market analysts for an automotive company randomly sampled five hundred new car buyers using a simple survey. This survey recorded the preferences of future consumers. The analysts documented several preferences in the same survey: engine size (i.e. an eight cylinder—V8—or a six cylinder—V6) and paint color. The data are present in the provided table.

What of the following correctly calculates the probability intersection future consumers that will want a car that is Black Pearl and has a V8?

8

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Thirty-three freshmen, ten sophomores, eight juniors, and twenty-two seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

9

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Thirty-three freshmen, ten sophomores, eight juniors, and twenty-two seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

10

Use the general multiplication rule to solve for the given probability model. For events A and B, calculate given the following information:

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