Conditional Probability and Independence Lesson Seed
S.CP.A.5 Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations.
MP3: Construct viable arguments and critique the reasoning of others.
MP8: Look for and express regularity in repeated reasoning.
Common Core Geometry, Unit 5
Background Information:
Students need to discuss similarities and differences between independent probability and
conditional probability in a real-world context. This discussion does not necessarily include
actual probabilities. Students need to understand that some conditional probabilities consist of
independent events. Students should be able to determine whether two events in a conditional
probability are independent of each other or conditional (dependent) by examining the effects
they have on each other.
Suggested Activity:
Assign students to groups of three or four. In their groups, have students work through the first
two discussion questions; define independent probability and conditional probability. Set up 10
stations, one for each probability discussion question. Have the groups circulate between the
stations to determine if the probability question is a true conditional probability or actually an
independent probability. Make sure the groups write why they think their answers are correct.
Students could write their answers on their own papers (so as not to let other groups see the
answers) or all of the groups could write the answers on the same paper (so the groups can see
each others’ answers). When everyone is finished, discuss the questions as a class in order to
clarify any misconceptions. (Look for evidence of MP3 and MP8 while students are answering
the questions.)
Discussion Questions:
What is independent probability?
Independent probability is when two or more events have outcomes that do not rely on each
other. Two examples of independent probability include “rolling a three on a number-cube” and
“getting a red space on a spinner”.
What is conditional probability?
Two events are considered to involve conditional probability when one event is affected by the
other.
P(pulling a red card from a deck|pulling a black card with replacement)
This is independent probability because the card was put back into the deck and so the sample
space
remained the same.
P(pulling a red card from a deck|pulling a red card without replacement)
This is conditional probability because the card was not put back into the deck and so the sample
space decreased which would yield a larger probability.
P(getting lung cancer|you are a smoker)
This is conditional because you are smoking and it has been proven that the likelihood of getting
lung cancer increases for smokers.
P(played football in college|play football for the NFL)
This is conditional probability because NFL players have to be a certain age and will more likely
continue to play a high level of football before entering the NFL which can be done in college.
P(playing football for the NFL|played football in college)
This is independent probability because a very small portion of college football players will go
on to play professionally.
P(flossing|brushed your teeth)
This is independent probability because simply brushing your teeth does not dictate that you will
floss.
P(you drive a car|you are at least 16)
This is independent probability because just being 16 does not dictate that you can drive a car.
You must also pass a test and have access to a car too.
P(you are at least 16|you drive a car)
This is conditional probability because you must be at least 16 in order to legally drive a car.
P(you live in Maryland|you live in Howard County)
This is conditional probability since Howard County is in Maryland.
P(you live in Howard County|you live in Maryland)
This is conditional probability. Even though there are other places you could live in Maryland,
the possibility of living in Howard County.