Worked examples
The question
Question: A coin is flipped 50 times and lands heads 28 times.
Find the experimental probability of heads.
1 Times it happened over times tried
It happened 28 times out of 50 flips.
So the experimental probability is 28/50.
P(heads) = 2850
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
28 and 50 can both be divided by 2.
So it is 14/25.
= 28 ÷ 250 ÷ 2 = 1425
As a percent: 25 times 4 is 100.
14 times 4 is 56.
So it is 56%.
= 14 × 425 × 4 = 56100 = 56%
2 Compare with the theory
In theory, a coin has 2 sides, so heads is 1 out of 2: 50%.
= theory: 12 = 50%
Careful!
That is the theory.
The question asks what really happened: 56%.
Careful: not P(heads) = 50% ✗
56% is close to 50%.
With more flips, it usually gets even closer.
= 56% > 50%
3 Check
Let's check: 56% of 50 flips should be the 28 times.
56% of 50 is 28.
So the answer is right!
56% of 50 = 28
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
Answer = 14 × 425 × 4 = 56100 = 56%
▶ Watch it solved
The question
Question: A die is rolled 60 times and 6 comes up 13 times.
Find the experimental probability of rolling a 6.
1 Times it happened over times tried
It happened 13 times out of 60 rolls.
So the experimental probability is 13/60.
P(a 6) = 1360
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
As a percent: 13 divided by 60, times 100, is about 21.7%.
= ≈ 21.7%
2 Compare with the theory
In theory, a die has 6 sides, so each number is 1 out of 6: about 16.7%.
= theory: 16 ≈ 16.7%
Careful!
That is the theory.
The question asks what really happened: 21.7%.
Careful: not P(a 6) = 16.7% ✗
21.7% is close to 16.7%.
With more rolls, it usually gets even closer.
= 21.7% > 16.7%
3 Check
Let's check: 21.7% of 60 rolls should be the 13 times.
21.7% of 60 is about 13.
So the answer is right!
21.7% of 60 = 13 ≈ 13
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
▶ Watch it solved
The question
Question: A die is rolled 90 times and 2 comes up 24 times.
Find the experimental probability of rolling a 2.
1 Times it happened over times tried
It happened 24 times out of 90 rolls.
So the experimental probability is 24/90.
P(a 2) = 2490
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
24 and 90 can both be divided by 6.
So it is 4/15.
= 24 ÷ 690 ÷ 6 = 415
As a percent: 4 divided by 15, times 100, is about 26.7%.
= ≈ 26.7%
2 Compare with the theory
In theory, a die has 6 sides, so each number is 1 out of 6: about 16.7%.
= theory: 16 ≈ 16.7%
Careful!
That is the theory.
The question asks what really happened: 26.7%.
Careful: not P(a 2) = 16.7% ✗
26.7% is close to 16.7%.
With more rolls, it usually gets even closer.
= 26.7% > 16.7%
3 Check
Let's check: 26.7% of 90 rolls should be the 24 times.
26.7% of 90 is about 24.
So the answer is right!
26.7% of 90 = 24 ≈ 24
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
▶ Watch it solved
