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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to separate observed frequency from certainty.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Fractions, decimals, and multiplication.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A spinner lands on blue 36 times in 120 recorded spins. Use the observations to estimate the probability of blue and predict an approximate count in 50 more spins.
Why this math matters
Relative frequency estimates a probability from observations but does not guarantee the next result. Report both the count and the total when presenting an experimental percentage.
Set up the model
A useful answer starts with clear assumptions:
- The spinner and spinning procedure remain comparable.
- The record includes every one of the 120 spins.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Separate observed frequency from certainty
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A spinner lands on blue 36 times in 120 recorded spins. Use the observations to estimate the probability of blue and predict an approximate count in 50 more spins.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
relative frequency = 36/120
Divide the observed blue count by the total recorded trials.
Apply the relationship
estimated P(blue) = 0.30
This is an empirical estimate, not proof of the spinner's exact probability.
Check and interpret
predicted count ≈ 50(0.30) = 15
Fifteen is a model-based expectation; an actual new set of spins can differ.
The result
predicted count ≈ 50(0.30) = 15
Fifteen is a model-based expectation; an actual new set of spins can differ.
Common mistakes to catch
- A larger number of trials can improve stability without removing bias in the procedure.
- An observed proportion is not a guaranteed proportion for the next batch.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A seed sprouts in 42 of 60 trials. Estimate the sprouting probability under comparable conditions.
Show a hint
Use successful trials divided by all trials.
Reveal answer and explanation
0.70
42/60 = 0.70; this is an estimate tied to the trial conditions.
Practice 2
Does an estimated probability of 0.70 guarantee exactly seven successes in the next ten trials?
Show a hint
Distinguish an average expectation from a fixed count.
Reveal answer and explanation
No
Random outcomes vary; 10(0.70) = 7 is a predicted average count, not a promise.
Take the idea with you
Report both the count and the total when presenting an experimental percentage.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: List compound outcomes before counting
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