7.SP.6: Estimate Probability from Repeated Trials
Also written as 7.SP.C.6 and CCSS.MATH.CONTENT.7.SP.C.6 · Cluster: Investigate chance processes and develop, use, and evaluate probability models.
The Official Wording
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 7.SP.6 Means in Plain English
Seventh graders estimate a probability by running a chance process many times. A thumbtack dropped 200 times lands point up 78 times, so the probability is about 78/200 = 0.39, a steadier estimate than the 18 of the first 50.
They also run it the other way: a number cube shows a 1 or 2 with probability 1/3, so 300 rolls should give about 100, probably not exactly. 7.SP.7 compares such frequencies with models, and high school tests models by simulation (HSS-IC.2).
7.SP.6 I Can Statements
- I can estimate a probability from the results of many trials.
- I can explain why more trials give a steadier estimate.
- I can predict about how often an outcome will happen.
7.SP.6 Worked Example
Data first, then a prediction: a thumbtack whose probability nobody can work out in advance, and a number cube whose probability everybody can.
A class dropped a thumbtack 200 times. It landed point up 18 times in the first 50 drops and 78 times in all 200. Estimate the probability of point up and predict the count in 500 drops. Then predict how often a 1 or 2 comes up in 300 rolls of a number cube.
- Relative frequency after the first 50 drops.18/50 = 0.36
- Relative frequency after all 200 drops. More trials give a steadier estimate, so use this one.78/200 = 0.39, so P(point up) ≈ 0.39
- Predict 500 drops by multiplying the probability by the number of trials.0.39 × 500 = 195 point up
- Now the other direction. A number cube has 6 equal faces, and 2 of them are a 1 or a 2.P(1 or 2) = 2/6 = 1/3; 1/3 × 300 = 100
- Both predictions are approximate: chance varies from run to run, so expect close to these counts, not exactly them.About 195 point up and about 100 ones and twos
Check it: The other outcome fills the rest: 122 of 200 landed point down, 0.61, and 0.39 + 0.61 = 1. A thumbtack is not a coin, so nothing forces either outcome to be 0.5.
Common Mistakes with 7.SP.6
Trusting a short run
After 10 drops, 6 landed point up, so P(point up) = 0.6
Try this: Keep adding trials and recompute; watch the relative frequency settle, 0.36 after 50 drops and 0.39 after 200.
Expecting the prediction exactly
300 rolls gave 94 ones and twos instead of 100, so the cube must be unfair
Try this: Expect results near the prediction, not on it; 94 against 100 is ordinary variation, while a count like 40 would be worth questioning.
Assuming two outcomes means one half
A thumbtack lands only two ways, so P(point up) = 1/2
Try this: Collect data before assigning a probability; two outcomes are equally likely only when the object is symmetric, like a fair coin.
Where 7.SP.6 Fits
Practice 7.SP.6
Quick Check
- A coin was tossed 80 times and landed heads 44 times. What is the relative frequency of heads?
- A spinner lands on red with probability 1/4. About how many reds should come up in 120 spins?
- A bottle cap landed top side up 33 times in 50 flips. Predict how many times it lands top side up in 400 flips.