Dependent Events Worksheet/Game

Dependent Events Worksheet/Game
Welcome to Dependent Events Worksheet/Game. Dependent events are occurrences where the outcome of the first event affects the probability of the second event, meaning the results are dependent. This usually happens in scenarios without replacement and the total number of outcomes or the composition of the sample space changes.

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

 

 

Probability of Dependent Events
The probability of dependent events is calculated as:
P(A and B) = P(A) × P(B|A)
where P(B|A) represents the conditional probability of event occurring, given that event has already happened.
This usually means that the “Total” (denominator) changes for the second pick.

How to play the Dependent Events Worksheet/Game

1. Read the Scenario:
   Each question describes a situation where an item is picked without replacement. This means the total number of items (the denominator) decreases after the first pick.
   

2. Calculate the Probability:
   Find the probability of the first event.
   Find the probability of the second event, keeping in mind that there is one less item in total.
   Multiply them together and simplify the fraction.
   

3. Choose an Option:
   Click the button that matches your simplified result.
   

4. Review the Math:
   If you get it right: You’ll see a success message and move on.
   If you get it wrong: A “Step-by-Step Solution” box will appear.
   

5. Finish the Marathon:
   Complete all 30 questions to see your final accuracy score.
   

Tip:
Look out for the words “without replacement” or it may also be implied in the question.

Sometimes the numerator and denominator of the second fraction will change.
Example: Picking 2 Red marbles (without replacement) from a bag of 6 (3 Red, 3 Blue).
Pick 1: \(\frac{3}{6}\) Pick 2: \(\frac{2}{5}\) (One red is gone, and the total marbles is reduced)
Result: \(\frac{3 \times 2}{6 \times 5} = \frac{6}{30} = {\frac{1}{5}}\)

Sometimes only the denominator of the second fraction will change.
Example: Picking 1 Red marble and 1 blue marble (without replacement) from a bag of 6 (3 Red, 3 Blue).
Pick 1: \(\frac{3}{6}\)
Pick 2: \(\frac{3}{5}\) (There are still 3 blue marbles, but the total marbles is reduced.)
Result: \(\frac{3 \times 3}{6 \times 5} = \frac{9}{30} = {\frac{3}{10}}\)

Dependent and Independent Events

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