Probability Tree Diagram Quiz

Probability Tree Diagram Quiz
Welcome to the Probability Tree Diagram Quiz. To learn how to use Tree Diagrams, you need to see how the “branches” split to represent every possible choice. In probability, each branch is labeled with its individual chance, and the final “leaves” represent the combined outcome.

In the following Probability Tree Quiz, you will be asked eight questions. You will need to multiply fractions along a path and may also need to add fractions along different paths. Scroll down the page for a more detailed explanation.

 

 

Probability Tree Diagram Quiz

1. Read the Scenario
   The first panel presents a “Visual Map.” In this specific setup:
   You start with 5 total marbles (3 Red, 2 Blue).
   Because it is a dependent scenario, picking one marble means it is not replaced. This is why the second set of branches shows a total of 4 marbles.
   

2. Trace the “Path”
   To solve any question in the quiz:
   Identify the outcome:
   If the question asks for “Red then Blue” (RB), find the branch starting with Red (3/5) and follow it to the next branch for Blue (2/4).
   Apply the Multiplication Rule:
   You multiply the fractions along the path you just traced.
   Example: 3/5 × 2/4 = 6/20.
   

3. Select and Simplify
   The quiz options are often simplified fractions.
   If your calculation results in 6/20, you must reduce it to 3/10 to find the matching button.
   If you select the wrong answer, a low-frequency “buzz” tone plays, and a step-by-step calculation appears in the feedback box to show you the correct logic.
   

4. “At least” questions
   To calculate the probability of “at least 1 Red” in this specific tree diagram lab, you are looking for any path that contains at least one Red marble. This includes the outcomes RR, RB, and BR.
   There are two main ways to solve this: the Addition Method and the Complement Method.
   

5. The Addition Method
   You can identify every individual path that meets the criteria and add their final probabilities together.
   Path RR: \(\frac{3}{5} \times \frac{2}{4} = \frac{6}{20}\)
   Path RB: \(\frac{3}{5} \times \frac{2}{4} = \frac{6}{20}\)
   Path BR: \(\frac{2}{5} \times \frac{3}{4} = \frac{6}{20}\)
   Total: \(\frac{6}{20} + \frac{6}{20} + \frac{6}{20} = \frac{18}{20}\) (which simplifies to 9/10).
   

6. The Complement Method (Shortcut)
   It is often easier to use the formula 1 - P(outcome you don’t want).
   In a scenario where you want “at least one Red,” the only outcome you don’t want is getting zero Reds (which is BB).
   Find the “Opposite” Path (BB):
   First Draw (Blue): \(\frac{2}{5}\)
   Second Draw (Blue): \(\frac{1}{4}\)
   \(P(BB) = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20}\)
   Subtract from 1: \(1 - \frac{2}{20} = \frac{18}{20}\)
   Simplify:
   \(\frac{18}{20}\) reduces to 9/10.
   Why use the Complement Method?
   This method is faster, especially as tree diagrams get larger. Instead of adding many different paths, you only have to calculate one and subtract.
   

7. To find the probability of getting exactly 1 Red and 1 Blue, you need to identify every path on the tree that ends with one of each color, regardless of the order.
   In this scenario, there are two specific paths that satisfy this condition:
   Red then Blue (RB)
   Blue then Red (BR)
   Step 1: Calculate the first path (RB)
   Follow the top branch to Red, then the bottom branch to Blue:
   First Draw (Red): 3/5
   Second Draw (Blue): 2/4
   Calculation: \(\frac{3}{5} \times \frac{2}{4} = \frac{6}{20}\)
   Step 2: Calculate the second path (BR)
   Follow the bottom branch to Blue, then the top branch to Red:
   First Draw (Blue): 2/5
   Second Draw (Red): 3/4
   Calculation: \(\frac{2}{5} \times \frac{3}{4} = \frac{6}{20}\)
   Step 3: Add the paths together
   Since either of these outcomes satisfies the “exactly 1 of each” rule, you add their probabilities:
   \(\frac{6}{20} + \frac{6}{20} = \frac{12}{20}\)
   Step 4: Simplify
   To find the final answer used in the lab, simplify the fraction:
   \(\frac{12}{20} = \frac{3}{5}\)
   Summary of the Rule: To find the probability of a single path, you multiply along the branches. To combine multiple valid paths, you add the results of those paths together.
   

Probability Tree Diagrams

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