Step by step
The question
Question: A die is rolled 36 times and 5 comes up 0 times.
Find the experimental probability of rolling a 5.
1 Times it happened over times tried
It happened 0 times out of 36 rolls.
So the experimental probability is 0/36.
P(a 5) = 036
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
As a percent: 1 times 100 is 100.
0 times 100 is 0.
So it is 0%.
= 0 × 1001 × 100 = 0100 = 0%
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: 0%.
Careful: not P(a 5) = 16.7% ✗
0% is far from 16.7%.
With so few rolls, that can happen.
More rolls usually get closer.
= 0% < 16.7%
3 Check
Let's check: 0% of 36 rolls should be the 0 times.
0% of 36 is 0.
So the answer is right!
0% of 36 = 0
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
Answer
= 0 × 1001 × 100 = 0100 = 0%