Probability Squad Slides Probability Squad
Mission: Independent Events
Analyze
Calculate
Verify
The Briefing
Definition
Events are independent if the first outcome does not change the next probability.
With Replacement
When we put it back, the odds stay exactly the same.
Rolling a die twice?
Independent!
Multiplication Rule
Probability of A AND B
P(A and B) = P(A) × P(B)
Step 1
Find P(A)
Step 2
Find P(B)
Step 3
Multiply!
Sample Mission
A bag has 3 Red and 7 Blue marbles. Pick one, replace it , pick again. What's the chance of Red, then Red?
1
P(Red) =
3 10
2
P(Red) =
3 10
GO
3 10
×
3 10
=
9 100
9%
Success Chance
Squad Practice
Discuss with your squad before the mission briefing ends.
"You spin a spinner with 4 equal sections (R, B, G, Y) and flip a coin."
What is P(Green and Heads)?
Analyze: What are Event A and B?
Calculate: P(A) and P(B)?
Practice Result
Checking the logistics...
Spinner P(G)
1 4
×
Coin P(H)
1 2
=
Total
1 8
Assign Roles
The Analyst
Identifies Event A, Event B, and the total sample space.
The Calculator
Determines the individual odds for P(A) and P(B).
The Strategist
Combines probabilities using the Multiplication Rule.
The Inspector
Checks the math, simplifies fractions, and verifies logic.
Mission starts now.
Probability Squad Worksheet Classified / Top Secret
Probability Squad
Operation: Independent Events (With Replacement)
Squad ID: ___________
Date: ___________
Analyst
Calculator
Strategist
Inspector
Objective Briefing
Multiply individual probabilities for independent events (with replacement): P(A) × P(B)
01
Mission: The Security Vault
"Draw a card from 10 cards (labeled 1-10) and put it back. Then, roll a 6-sided die . What is the probability of drawing a 7 AND rolling an even number ?"
Step 1: Analyst
Define Events A & B:
A: ________________________
Step 2: Calculator
Probabilities:
P(A) __/ __
P(B) __/ __
Step 3: Strategist
The Multiplication:
___ × ___ = ___
Step 4: Inspector
Final Verification:
02
Mission: Supply Drop
"A supply crate has 5 rations , 3 first-aid kits , and 2 water filters . Pull one, put it back, then pull a second. What is the probability of pulling two first-aid kits ?"
Analyst: Total Sample Space
Rations: _____ First-aid: _____ Filters: _____ TOTAL: _____
Calculator: Probabilities
P(1st) __/ __
P(2nd) __/ __
Strategist: Calculation Area
Inspector Report
03
Challenge: Codebreaker
"Guess a 2-character passcode. Char 1 is a letter (A-Z) . Char 2 is a digit (0-9) . Probability of a passcode that starts with a vowel (A, E, I, O, U) and ends with an odd number ?"
Analyst & Calculator Area
P(Vowel):
Show your work...
P(Odd Digit):
Show your work...
Strategist
Multiplication Strike Zone
Inspector Certification Center
Final Fraction
Simplified
Percent (%)
Official Squad Seal:
Probability Squad Answer Key Teacher Access Only
Answer Key
Operation: Probability Squad Mission
Resource: Teacher Guide
Subject: Independent Events
KEY Mission 01: The Security Vault
Step 1 (Analyst):
Step 2 (Calculator):
Step 3 (Strategist):
Step 4 (Inspector): 1/20 5%
KEY Mission 02: Supply Drop
Step 1 (Analyst):
Step 2 (Calculator):
Step 3 (Strategist):
Step 4 (Inspector): 9/100 9%
! Final Challenge: Codebreaker
Step 1 & 2 (Logic Check)
Event A (Vowel): {A, E, I, O, U} (5 total)P(Vowel) = 5/26
Event B (Odd Digit): {1, 3, 5, 7, 9} (5 total)P(Odd) = 5/10 = 1/2
Multiplication Strike
5/26 × 1/2 = 5/52
Final Validation
5/52
Approx. 0.096
9.6%
MISSION DEBRIEF: Watch for the 'Codebreaker' sample space—many students forget '0' is a digit. Replacement is the key concept here; ensure students don't reduce the denominator for the second event.
