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

Instructions

Probability helps us understand the chance of something happening. For each problem below, read the scenario and compare the two possible outcomes. Decide which outcome is more likely to happen, or if they are equally likely. Circle your answer and write a short sentence explaining why.

1. You roll a standard six-sided die once.

   Outcome A: Rolling a number less than 3 (the numbers 1 or 2).

   Outcome B: Rolling a number greater than 4 (the numbers 5 or 6).

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________




2. A bag contains different colored marbles: 10 green, 6 blue, and 4 red. You reach in and pull one marble out without looking.

   Outcome A: Pulling out a green marble.

   Outcome B: Pulling out a blue or a red marble.

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________




3. A spinner is divided into 8 equal sections. 4 of the sections are yellow, 3 are purple, and 1 is white.

   Outcome A: The spinner lands on yellow.

   Outcome B: The spinner lands on a color that is not yellow.

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________




4. You have a standard deck of 52 playing cards (no jokers).

   Outcome A: Drawing a face card (Jack, Queen, or King).

   Outcome B: Drawing a numbered card from 2 to 5 (2, 3, 4, or 5).

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________




5. A school cafeteria offers three lunch options with the following popularity: Pizza (chosen by 55% of students), Tacos (chosen by 30%), and Salad (chosen by 15%).

   Outcome A: A randomly chosen student picked Pizza.

   Outcome B: A randomly chosen student picked either Tacos or Salad.

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________




6. You are watching your friend play a video game. To win, she needs to either find a rare gem (1 in 20 chance) or defeat a mini-boss (1 in 10 chance) on her next turn.

   Outcome A: She finds the rare gem.

   Outcome B: She defeats the mini-boss.

   Which outcome is more likely, A or B, or are they equally likely?

   __________________________________________________________________

   Explanation: __________________________________________________________________

Answer Key

1. Equally likely.

   Explanation: There are two ways to get Outcome A (rolling a 1 or 2) and two ways to get Outcome B (rolling a 5 or 6). Since the number of favorable outcomes is the same for both, they are equally likely.

2. Equally likely.

   Explanation: There are 10 green marbles (Outcome A). The number of marbles that are blue or red is 6 + 4 = 10 (Outcome B). Since both outcomes have 10 possible marbles, they are equally likely.

3. Equally likely.

   Explanation: There are 4 yellow sections (Outcome A). The number of sections that are not yellow is 3 (purple) + 1 (white) = 4 sections (Outcome B). The chances are the same.

4. Outcome B is more likely.

   Explanation: There are 3 types of face cards (J, Q, K) and 4 suits, so there are 3 x 4 = 12 face cards in the deck. There are 4 numbered cards listed (2, 3, 4, 5) and 4 suits, so there are 4 x 4 = 16 of those numbered cards. Since 16 is greater than 12, Outcome B is more likely.

5. Outcome A is more likely.

   Explanation: The chance of a student picking Pizza is 55%. The chance of a student picking Tacos or Salad is 30% + 15% = 45%. Since 55% is greater than 45%, Outcome A is more likely.

6. Outcome B is more likely.

   Explanation: A 1 in 10 chance is greater than a 1 in 20 chance. Think of it as fractions: 1/10 is larger than 1/20. Therefore, it is more likely that she will defeat the mini-boss.