Probability Worksheet for 13-Year-Olds: Identifying Which Outcomes Are More Likely (Middle School Math)

Instructions

Read each scenario carefully. Your goal is to compare the chances of different events happening. Use terms like "more likely," "less likely," "equally likely," "certain," or "impossible" to describe the outcomes. For some questions, you will need to calculate the simple probability (chance) of an event. Good luck!

Probability reminder: Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Part 1: The Gumball Machine

A gumball machine contains the following gumballs: 12 Red, 8 Blue, 8 Green, and 2 Yellow.

For each question, circle the more likely outcome or write "equally likely."

1. Getting a Red gumball OR Getting a Blue gumball


2. Getting a Green gumball OR Getting a Blue gumball


3. Getting a Yellow gumball OR Getting a Red gumball


4. Which color gumball are you least likely to get? _______________

Part 2: Rolling a Die

Imagine you are rolling a standard, fair six-sided die one time. The numbers on the faces are 1, 2, 3, 4, 5, and 6. Answer the following questions.

1. Which event is more likely?
   • Event A: Rolling an even number (2, 4, 6).
   • Event B: Rolling a number greater than 3 (4, 5, 6).

   Explain your reasoning:

   __________________________________________________________________



2. Which event is more likely?
   • Event C: Rolling a 5.
   • Event D: Rolling a number that is a multiple of 3 (3, 6).

   Calculate the probability for both events to prove your answer.

   P(Event C) = _____

   P(Event D) = _____



3. Describe the likelihood of rolling a 7. (Use one of the key terms: certain, impossible, likely, etc.)

___________________

Part 3: Spinner Challenge

A spinner is divided into 10 equal sections, as described below:

• 4 sections are labeled "Win"
• 3 sections are labeled "Try Again"
• 2 sections are labeled "Lose a Turn"
• 1 section is labeled "Bonus Prize"

Analyze the likelihood of the following events based on one spin.

1. Is it more likely that you will "Win" or "Try Again"?

___________________



2. Which is more likely: landing on "Lose a Turn" or landing on "Bonus Prize"?

___________________



3. Combine the sections. Is it more likely that you will land on a positive space ("Win" or "Bonus Prize") or a negative space ("Try Again" or "Lose a Turn")? Show your work to justify your answer.

Probability of a positive space: __________

Probability of a negative space: __________

Conclusion: _________________________________________________

Part 4: Word Play

Look at the letters in the word: M A T H E M A T I C S

If you were to close your eyes and point to one letter at random, which of the following outcomes would be more likely? Circle your answer.

1. Pointing to the letter 'M' OR Pointing to the letter 'T'


2. Pointing to a vowel (A, E, I) OR Pointing to a consonant (M, T, H, C, S)


3. Pointing to the letter 'A' OR Pointing to the letter 'S'

Answer Key

Part 1: The Gumball Machine

1. Getting a Red gumball (12 Red vs. 8 Blue)
2. Equally likely (8 Green vs. 8 Blue)
3. Getting a Red gumball (12 Red vs. 2 Yellow)
4. Yellow (It has the fewest number of gumballs)

Part 2: Rolling a Die

1. Equally likely
   Explanation: Both events have 3 possible outcomes. Event A (2, 4, 6) has 3 outcomes. Event B (4, 5, 6) also has 3 outcomes. Their probabilities are both 3/6 (or 1/2).
2. Event D is more likely.
   P(Event C) = 1/6
   P(Event D) = 2/6 (or 1/3)
3. Impossible (A standard die only has numbers 1-6).

Part 3: Spinner Challenge

1. It is more likely that you will "Win" (4/10 chance vs. 3/10 for "Try Again").
2. It is more likely you will land on "Lose a Turn" (2/10 chance vs. 1/10 for "Bonus Prize").
3. Probability of a positive space: "Win" (4) + "Bonus Prize" (1) = 5 sections. P(positive) = 5/10 (or 1/2)
   Probability of a negative space: "Try Again" (3) + "Lose a Turn" (2) = 5 sections. P(negative) = 5/10 (or 1/2)
   Conclusion: It is equally likely that you will land on a positive space or a negative space.

Part 4: Word Play

Total letters = 11. M=2, A=2, T=2, H=1, E=1, I=1, C=1, S=1. Vowels=4, Consonants=7.

1. Equally likely (There are two 'M's and two 'T's).
2. Pointing to a consonant (There are 7 consonants vs. 4 vowels).
3. Equally likely (There are two 'A's and two 'S's).