Taking a Chance: Compound Probability

Introduction (5 minutes):

Review Simple Probability: Start by reviewing the basic concept of probability:

Probability: The likelihood of an event occurring. It's expressed as a number between 0 (impossible) and 1 (certain).
Formula: Probability = (Favorable Outcomes) / (Total Possible Outcomes)
Example: What's the probability of rolling a 5 on a standard die? (1/6)
Introduce Compound Events: Explain that compound events involve two or more simple events happening together.

Example: Rolling a die AND flipping a coin.
 

Activity 1: Independent Events (15 minutes)

Define Independent Events: Events are independent if the outcome of one does NOT affect the outcome of the other.
Example: Flipping a coin and rolling a die.
Calculate Probability:
Multiply Rule: To find the probability of two independent events happening, multiply the probability of each event.
Example: What's the probability of flipping heads AND rolling a 4?
P(heads) = 1/2
P(rolling a 4) = 1/6
P(heads AND rolling a 4) = (1/2) * (1/6) = 1/12
Hands-on Practice: Have students work in pairs to calculate probabilities of independent events using dice, coins, or other manipulatives.
Example: What's the probability of drawing a red card from a deck, replacing it, and then drawing another red card?
 

Activity 2: Dependent Events (15 minutes)

Define Dependent Events: Events are dependent if the outcome of the first event DOES affect the outcome of the second.
Example: Drawing a card from a deck and NOT replacing it before drawing another card.
Calculate Probability:
Modified Multiply Rule: Calculate the probability of the first event. Then, calculate the probability of the second event given that the first event has already happened. Multiply these probabilities.
Example: What's the probability of drawing a king from a deck, NOT replacing it, and then drawing another king?
P(drawing a king) = 4/52 = 1/13
P(drawing another king, given the first king is gone) = 3/51 = 1/17
P(drawing a king AND then another king) = (1/13) * (1/17) = 1/221
Hands-on Practice: Have students work in pairs to calculate probabilities of dependent events using cards, marbles, or other manipulatives.
Example: What's the probability of drawing a blue marble from a bag with 3 blue and 5 red marbles, not replacing it, and then drawing another blue marble?
 

Wrap-up (5 minutes):

Review the key differences between independent and dependent events.
Discuss how compound probability can be used to analyze real-world situations (e.g., predicting the outcome of a game, understanding risk in different scenarios).
 

Assessment:

Observe student participation and provide feedback during the activities.
Collect student work and assess their understanding of calculating and interpreting compound probabilities.
Assign word problems involving independent and dependent events for homework.

differentiation: Provide visual aids like tree diagrams to help them visualize the different outcomes.

extension: Challenge them with more complex compound events involving three or more simple events or with scenarios that require them to determine whether events are independent or dependent.

Use the performance task linked in the resources tab to assess student learning outcomes.