6th grade · Math · Unit 9 of 21
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.
New York State Learning Standards learning standard: NY-6.SP.6; NY-6.SP.7; NY-6.SP.8 · probability as a number from 0 to 1, comparing experimental and theoretical probability, and simple probability models
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 New York
In the New York State Learning Standards, this is unit 9 of 21 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
You roll a fair 6-sided die numbered 1 to 6. What is the probability of rolling a multiple of 4?
answer box
1/6
Hint: List the outcomes that work: 4. Write how many there are over the 6 equally likely outcomes.
Question 2
Kenji flips a fair coin 20 times and gets 14 heads. Which statement is true?
- The experimental probability of heads (14/20) is lower than the theoretical probability (1/2).
- The experimental probability of heads (14/20) is higher than the theoretical probability (1/2).
- The theoretical probability of heads is 14/20.
- The coin must be unfair.
The experimental probability of heads (14/20) is higher 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.
Question 3
A bag holds the marbles in the table. You pick one without looking. What is the probability it is green?
Marbles in the bag Color Number 🟢 green 1 🟡 yellow 4 🟣 purple 8 - 4/13
- 12/13
- 1/13
- 1/12
1/13
Hint: Probability = marbles of that color ÷ all the marbles. Add up every marble in the table to find the total first.
Question 4
Kenji flips a coin 50 times and gets heads 20 times. What is the experimental probability of heads?
answer box
20/50
Hint: Experimental probability = number of times it happened ÷ total number of trials.
Question 5
If you spin this spinner 60 times, about how many times would you expect it to land on blue?
answer box
12
Hint: The theoretical probability of blue is blue sections ÷ 5. Find that fraction of 60: divide 60 by 5, then multiply by the number of blue sections.
Question 6
The spinner has 8 equal sections. What is the probability of landing on green?
answer box
6/8
Hint: Probability = favorable outcomes ÷ total outcomes. Count the green sections and write that number over 8.