St. James 04-23-2025 Probability

​Take out your notes/graphic organizer

🎯 Objectives:

• I can determine if events are independent or dependent.

• I can calculate conditional probability in real-world contexts.

• I can apply geometric models (like area) to calculate probability.

Probability

​***Uniform Sample Space = equal chance for all outcomes***

Independent Compound
Events

The events DO NOT affect each other (marbles in a bag)

The item is REPLACED
(Marble is put back in bag)

Dependent Events

The events DO AFFECT each other

The item is NOT REPLACED
(Marble is NOT put back)

The Addition Rule

Multiplication Rule

Open Ended

Coin Toss Decision 🪙

You flip a coin to decide who goes first in a game.
What is the probability it lands on heads? (Express as a fraction)

Open Ended

Rolling for a Prize 🎲

In a contest, you win if you roll an odd number on a standard die.
What is the probability of winning? (Fraction)

Open Ended

Lottery Wheel Spin 🎡

A lottery wheel has 8 equal slots numbered 1–8.
What is the probability it lands on number 7? (Fraction)

Open Ended

Drawing a King for Bonus Points 🃏

You draw a card from a standard deck.
What is the probability of drawing a king? (Fraction)

Open Ended

Color Raffle – Red or Blue Ticket 🎟️

A raffle has 26 red and 13 blue tickets in a box of 52 tickets.
What’s the probability of drawing a red or blue ticket? (Fraction)

Open Ended

You draw one card.
What’s the probability of drawing a heart or an ace? (Decimal, round to hundredth)

Open Ended

Rolling Double Sixes in a Game 🎲

You roll two dice.
What’s the probability of rolling two sixes? (Fraction)

Open Ended

You have 5 red socks and 3 blue socks. You randomly grab two without replacement.
What’s the probability both are blue? (Fraction)

Open Ended

Garden Plot 🌻

A rectangular garden is 200 ft². A flower bed takes up 50 ft².
What is the probability a randomly tossed seed lands in the flower bed? (Decimal)

Open Ended

Coin Flip & Dice Roll Combo 🎲🪙

You flip a coin and roll a die.
What’s the probability of getting tails AND rolling a 4? (Fraction)

Open Ended

Drawing Two Aces Without Replacement 🃏

You draw 2 cards from a deck without replacement.
What is the probability both cards are aces? (Fraction)

Open Ended

Playground Sandpit 🏖️

A playground is 300 m². The sandpit is 75 m².
What is the probability a child randomly stands in the sandpit? (Percent)

Open Ended

Survey – Club Membership 🎓

In a school of 40 students:

18 are in Drama

15 are in Music

5 are in both

What’s the probability a student is in Drama or Music? (Fraction)

Open Ended

Drawing a Face Card 🂫

You draw one card.
What’s the probability it’s a face card? (Fraction)

Open Ended

Carnival Dart Game 🎯

A board is 144 in². The prize zone is 36 in².
What’s the probability of hitting the prize zone? (Fraction)