Filter Focus Slides TIER 2 INTERVENTION
The Focus Filter
Mastering Conditional Probability P(A|B)
Isolate the Condition
Fractional Thinking
What is "Given B"?
When we see P(A | B), we ask:
"Out of only the times B happens, how often does A also happen?"
1
Ignore everything outside of Circle B.
2
Circle B is now our Whole Universe.
A & B
B
Entire Sample Space
Step-by-Step Discovery
1. Identify "The Given"
P(A | Blue)
Circle the "B" condition. This is your Denominator.
2. Find the Overlap
P(Both | Blue)
Identify outcomes in A and B. This is your Numerator.
3. The Final Ratio
Calculation
A ∩ B
B
Divide the "Both" part by the "Condition" whole.
Case Study: The Sports Filter
Group Plays Sport No Sport Sophomores 12 18 Juniors 15 25
Question: Find P(Plays Sport | Junior)
1. Apply the Filter
Condition: "Junior". Highlight that row.
Total Juniors = 15 + 25 = 40
2. Find the Success
How many in that row "Play Sport"?
Sport & Junior = 15
3. Interpretation
15 / 40 = 3/8 (37.5%)
"Of all the Juniors, 3/8ths play a sport."
Your Turn!
In a survey of 100 students, 30 are in Band, 20 are in Drama, and 10 are in both.
Find P(Drama | Band)
Step A: What is the denominator (the condition)?
Step B: How many fit both criteria?
Outcome Tracker Worksheet Outcome Tracker
Focusing the Sample Space
Name:
Date:
1
Visualize the "Given"
When finding P(A | B), we ignore everything that is NOT in B. Think of Circle B as your new "Zoomed-In" world.
Step 1: Circle "The Given" (B)
A
B
Step 2: Find the "Success"
Both
2
Guided Venn Calculation
School Clubs Data
Chess
Robotics
12 8 20 Neither: 15
Find P(Chess | Robotics)
Step A: The Denominator (Total Robotics)
=
Step B: The Numerator (Both Chess & Robotics)
Step C: Final Ratio
=
3
Data Table Filter
Likes Pizza Dislikes Total 9th Grade 45 5 50 10th Grade 38 12 50
Target Question:
"Find the probability that a student likes pizza, given they are in the 10th grade."
1. How many 10th graders like pizza? (The Success)
2. Calculate the Ratio:
=
3. Interpretation:
Out of all the ________ grade students, ________ out of ________ like pizza. This probability is ________.
Probability Probe Exit Ticket Probability Probe
Quick Check: The Focus Filter
Student:
Date:
1
Venn Diagram Filter
Soccer
Band
15 5 20
Find P(Soccer | Band):
Fraction:
/
Decimal:
2
Table Isolate
Has Pet No Pet Total Bus Riders 18 12 30 Walkers 14 6 20
"Given a student is a Bus Rider, find the probability they have a pet."
Calculation Area:
Interpretation (Write a sentence):
Hard
Okay
Easy
Intervention Intel Teacher Guide Intervention Intel
Teacher Support Guide
Lesson: The Focus Filter
Core Objective
Students will calculate the conditional probability of A given B by restricting the sample space to B and finding the fraction of B that is also in A.
Colorado Standard
HS.S-CP.B.6
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A.
Common Misconceptions
The Denominator Trap
Students often use the total population (e.g., 100 students) as the denominator instead of the conditioned group (e.g., just the 20 students in Band).
The Both/Either Mixup
Confusion between "A and B" (intersection) and "A or B" (union). Emphasize that for conditional probability, the numerator is always the intersection of the two sets.
Facilitation Script & Prompts
Q1:
"Look at the word 'Given.' What does that tell us about our world?"
Goal: Students identify that the world has "shrunk" to only include the given condition.
Q2:
"If we only look at the 'Band' circle, how many people are in our 'new' total?"
Goal: Discourage looking at numbers outside the specified circle.
Q3:
"Out of that band group, who also plays soccer? Where is that in our diagram?"
Goal: Direct focus to the intersection as the success criteria.
Master Answer Key
Outcome Tracker Worksheet
Venn Problem:
Step A (Denominator): 8 + 20 = 28
Step B (Numerator): 8
Step C (Ratio): 8 / 28 = 2/7 (≈ 28.6%)
Table Problem:
Filter: 10th Grade Row
Success: 38 (Likes Pizza)
Total: 50
Ratio: 38/50 = 19/25 (or 76%)
Probability Probe (Exit Ticket)
Problem 1:
P(Soccer | Band) = Intersection (5) / Total Band (20+5) = 5/25 or 1/5 (0.2).
Problem 2:
Condition: Bus Riders (30 total).
Success: Bus Riders with Pet (18).
Ratio: 18/30 = 3/5 (0.6).
"Out of all Bus Riders, 18 out of 30 have a pet. This is 60%."
