Concept Byte: Conditional Probability

Use With Lesson 12-8

ACTIVITY

A conditional probability contains a condition that may limit the sample space for an event. You can write a conditional probability using the notation P (B | A), read “the probability of event B, given event A.”

Activity 1

The table shows sales at a car dealership. Use the table to answer the following questions.

1. How many domestic cars were sold?
2. How many foreign cars were sold?
3. How many cars were sold for $15,000 or less?
4. How many cars were sold for more than $15,000?

To find a conditional probability like P(domestic | $15,000 or less), which is the probability that a car is domestic given it costs $15,000 or less, first determine the sample space. There are 26 cars that are $15,000 or less. Of those 26 cars, 15 are domestic. So, P(domestic | $15,000 or less) = 15 26 . 15 over 26 , .

5. 1. What is P(foreign | $15,000 or less) and P($15,000 or less | foreign)?
   2. Reasoning Are the probabilities the same? Why or why not?
6. Data Collection Conduct a survey of at least ten people. Find out if they are right- or left-handed. Also find out if each person has any left-handed family members.
   1. Copy the table below and record your data.

      	Left-Handed Family Members	No Left-Handed Family Members
      Left-handed	____	____
      Right-handed	____	____

   2. Find P(left-handed | left-handed family members).
   3. Find P(no left-handed family members | left-handed).
   4. Interpret your results.
7. Reasoning Consider the theoretical probabilities for a pair of number cubes. Does P(even on cube 1 | odd on cube 2) = P(odd on cube 2 | even on cube 1)? Explain your answer.
8. Consider the table below. Find each probability.

   Projected Number of Degree Recipients in 2015 (thousands)

   Degree	Male	Female
   Associate's	288	467
   Bachelor's	720	980
   Advanced	377	506

   SOURCE: U.S. Department of Education

   1. P(female recipient | associate's degree)
   2. P(male recipient | bachelor's degree)
   3. P(advanced degree | female recipient)
   4. P(female recipient | advanced degree)

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