6th grade · Math · Unit 9 of 17
Probability
Theoretical and experimental chance
What your child practices
Writing probabilities as fractions for spinners, dice and marbles, comparing theoretical probability with experimental results, and making predictions from data.
Minnesota K-12 Academic Standards benchmark: 6.1.2.2; 6.1.2.3 · theoretical and experimental probability
How we explain it
Children can open this short lesson before they practice.
- Probability = favorable outcomes ÷ all possible outcomes.
- It can be written as a fraction, a decimal or a percent.
- Experimental probability comes from trials. Theoretical comes from counting outcomes.
Example: A die is rolled. What is the probability of an even number? Even numbers: 2, 4, 6. That is 3 outcomes. There are 6 outcomes in all. 3/6 = 1/2. Answer: 1/2
Probability in Minnesota
In the Minnesota K-12 Academic Standards, this is unit 9 of 17 in 6th grade Math, after Volume & Capacity and before Integers & Decimals.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Where does this event belong on a probability line from 0 to 1: rolling a 1 on a 20-sided die?
- 1 (certain)
- 1/2 (equally likely)
- Close to 1 (likely)
- Close to 0 (unlikely)
- 0 (impossible)
Close to 0 (unlikely)
Hint: 0 means it can never happen and 1 means it is certain. 1/2 means it is just as likely to happen as not.
Question 2
A bag holds the marbles in the table. You pick one without looking. What is the probability it is red?
Marbles in the bag Color Number 🟡 yellow 8 🔵 blue 7 🔴 red 6 - 6/15
- 6/21
- 8/21
- 1/3
6/21
Hint: Probability = marbles of that color ÷ all the marbles. Add up every marble in the table to find the total first.
Question 3
The spinner has 6 equal sections. What is the probability of landing on red?
answer box
4/6
Hint: Probability = favorable outcomes ÷ total outcomes. Count the red sections and write that number over 6.
Question 4
You roll a fair 6-sided die numbered 1 to 6. What is the probability of rolling a 5?
answer box
1/6
Hint: List the outcomes that work: 5. Write how many there are over the 6 equally likely outcomes.
Question 5
Jay takes 50 basketball free throws and makes 36 of them. What is the experimental probability of making a shot?
answer box
36/50
Hint: Experimental probability = number of times it happened ÷ total number of trials.
Question 6
Jay flips a fair coin 20 times and gets 7 heads. Which statement is true?
- The experimental probability of heads (7/20) is lower than the theoretical probability (1/2).
- The experimental probability of heads (7/20) is higher than the theoretical probability (1/2).
- The theoretical probability of heads is 7/20.
- The coin must be unfair.
The experimental probability of heads (7/20) is lower than the theoretical probability (1/2).
Hint: Theoretical probability comes from equally likely outcomes: heads is 1 of 2. Experimental probability comes from real results, which often differ a little, especially with fewer trials.