Mathematics
Grade 11
15 min
Find conditional probabilities using two-way frequency tables
Find conditional probabilities using two-way frequency tables
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1
Introduction & Learning Objectives
Learning Objectives
Interpret data organized in a two-way frequency table.
Define conditional probability and its notation, P(A|B).
Calculate conditional probabilities directly from the counts in a two-way frequency table.
Distinguish between the probabilities P(A|B) and P(B|A).
Use the conditional probability formula to verify calculations made from a table.
Apply conditional probability to determine if two events are independent.
Solve real-world problems involving conditional probability using two-way tables.
Ever wonder how a streaming service recommends a movie you actually like? 🎬 They use conditional probability to predict what you'll enjoy based on your viewing history!
This tutorial will teach you how to use two-way frequency tables to organize data and fin...
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Key Concepts & Vocabulary
TermDefinitionExample
Two-Way Frequency TableA table that displays the frequency distribution of two categorical variables. The rows show the categories for one variable, and the columns show the categories for the other.A table showing the number of students surveyed, categorized by their grade level (9th, 10th, 11th, 12th) and their primary mode of transportation to school (Bus, Car, Walk).
Joint FrequencyEach cell within the body of a two-way table that shows the count of outcomes for a specific combination of the two variables.In a school transportation table, the number of 11th graders who ride the bus to school is a joint frequency.
Marginal FrequencyThe totals for each row and each column in a two-way table. They represent the total frequency for each category of a single variable,...
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Core Formulas
Conditional Probability from a Table (Counts Method)
P(A|B) = (Frequency of A and B) / (Marginal Frequency of B)
This is the most direct way to find conditional probability from a table. The numerator is the joint frequency (the cell where A and B intersect), and the denominator is the marginal frequency (the total for the row or column of the 'given' event B).
Formal Conditional Probability Formula
P(A|B) = P(A \cap B) / P(B)
This is the formal definition. P(A and B) is the probability of both events happening, and P(B) is the probability of the given event happening. When using a table, P(A and B) = (Joint Frequency)/(Grand Total) and P(B) = (Marginal Frequency of B)/(Grand Total). The 'Grand Total' terms cancel out, resulting in the Counts Method formu...
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Challenging
A survey of 200 students finds that 120 are in a club and 80 are not. The probability that a student is in a club, given they are on the honor roll, is 0.75. If there are 100 students on the honor roll, how many students are both in a club and on the honor roll?
A.90
B.75
C.100
D.60
Challenging
At a school with 400 students, 180 play a sport. Of the students who play a sport, 150 have a GPA of 3.0 or higher. Of the students who do not play a sport, 110 have a GPA of 3.0 or higher. What is the probability that a student plays a sport, given they have a GPA of 3.0 or higher?
A.15/26
B.15/18
C.18/40
D.26/40
Challenging
To determine if 'owning a laptop' (L) and 'being a senior' (S) are independent events among high school students, which of the following comparisons must be made?
A.Compare P(L ∩ S) with P(L U S)
B.Compare P(L|S) with P(S|L)
C.Compare P(L|S) with P(L)
D.Compare P(L) with P(S)
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