Independent & Dependent Events Worksheet/Game

Independent & Dependent Events Worksheet/Game
Welcome to Independent & Dependent Events Worksheet/Game. Independent events are occurrences where the outcome of the first event does not affect the probability of the second (e.g., flipping a coin, rolling dice). Dependent events are those where the first event does change the probability of the second (e.g., picking cards without replacement).

This game is designed to test your ability to calculate the probability of independent & dependent events. Scroll down the page for a more detailed explanation.

Independent & Dependent Events are AND events.
Check out this other worksheet/game for OR Events.

 

 

Differences between Independent and Dependent Events
Definition:
Independent Events: The occurrence of one event does not change the probability of the other.
Dependent Events: The occurrence of one event affects the probability of the subsequent event.

Probability Formulas:
Independent: P(A and B) = P(A) × P(B)
Dependent: P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A occurred.

Replacement Scenarios:
Independent: Generally involves scenarios with replacement, where the sample space remains the same.
Dependent: Often involves scenarios without replacement, where the sample space changes (e.g., drawing cards, taking marbles from a bag).

How to play the Independent & Dependent Events Worksheet/Game

1. Identify the Event Type
   When a question appears, look for “trigger words” to decide how to calculate the answer:
   Independent: Look for “replaces it,” “with replacement,” or events that naturally don’t affect each other (like flipping a coin and rolling a die). The total number of items stays the same for both events.
   Dependent: Look for “without replacement,” “keeps it,” “eats it,” or “loses it.” These actions reduce the total number of items for the second event.
   

2. Do the Math
   You need to multiply the probability of the first event by the probability of the second.
   Example (Independent): Drawing a King, replacing it, then an Ace.
   \(\frac{4}{52} \times \frac{4}{52} = \frac{1}{13} \times \frac{1}{13} = 1/169\)
   Example (Dependent): Picking two red pens from 10 (where 3 are red) without replacement.
   \(\frac{3}{10} \times \frac{2}{9} = \frac{6}{90} = 1/15\)
   

3. Select the Simplified Answer
   The four buttons will show simplified fractions. If your calculation results in \(\frac{6}{90}\) and you don’t see it, try simplifying the fraction (dividing both numbers by their greatest common factor) to find the match.
   

4. Review the “Calculation Box”
   If you get a question wrong, a Calculation Box will appear. This is the an important part of the game for learning. It shows you exactly how the two fractions were multiplied to reach the correct answer.
   

Dependent and Independent Events

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