Cogito
Grade 7 Math · Chapter 9 · Lesson 4
What Actually Happened
Experimental probability against theoretical.
10 problems · about 19 minutes · 7.SP.C.6, 7.SP.C.7
What this lesson teaches
The child compares observed frequencies with theoretical probability and explains the gap.
- Theoretical probability is counted; experimental probability is observed.
- A gap between them is normal, especially with few trials.
- The more trials, the closer the observed fraction usually gets.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Probability as a Number: A die. How many outcomes give a number above 4?
Answer 2
Why 2 out of 6.
Review — Samples and What They Tell You: 9 of 30 sampled. In 300, about how many?
Answer 90
Why About 90.
Review — Probability as a Number: A fair die. Out of 6, how many outcomes are less than 3?
Answer 2
Why 2 out of 6.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA fair die rolled 120 times. About how many threes are expected?
Answer 20
Why About 20.
A fair die rolled 60 times. About how many sixes are expected?
Answer 10
Why One sixth of 60.
50 spins give 30 reds. How many were not red?
Answer 20
Why 50 − 30.
Build It Up
The same ideas with more to keep track of.
2 problemsDoes 7 heads in 10 prove a coin is unfair? 1 for yes, 0 for no.
Answer 0
Why Small samples wander.
Do more trials usually bring the two closer? 1 for yes, 0 for no.
Answer 1
Why The long run.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Flips: 20 flips give 12 heads. How many gave tails?
Answer 8
Why 8.
The Expectation: A fair coin flipped 60 times. About how many heads are expected?
Answer 30
Why About 30.