Step by step
The question
Question: A die is rolled 120 times and 3 comes up 17 times.
Find the experimental probability of rolling a 3.
1 Times it happened over times tried
It happened 17 times out of 120 rolls.
So the experimental probability is 17/120.
P(a 3) = 17120
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
As a percent: 17 divided by 120, times 100, is about 14.2%.
= ≈ 14.2%
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: 14.2%.
Careful: not P(a 3) = 16.7% ✗
14.2% is close to 16.7%.
With more rolls, it usually gets even closer.
= 14.2% < 16.7%
3 Check
Let's check: 14.2% of 120 rolls should be the 17 times.
14.2% of 120 is about 17.
So the answer is right!
14.2% of 120 = 17 ≈ 17
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
Answer
= ≈ 14.2%