Step by step
The question
Question: A coin is flipped 30 times and lands tails 11 times.
Find the experimental probability of tails.
1 Times it happened over times tried
It happened 11 times out of 30 flips.
So the experimental probability is 11/30.
P(tails) = 1130
Experimental probability comes from what really happened in the experiment.
experimental = what really happened
As a percent: 11 divided by 30, times 100, is about 36.7%.
= ≈ 36.7%
2 Compare with the theory
In theory, a coin has 2 sides, so tails is 1 out of 2: 50%.
= theory: 12 = 50%
Careful!
That is the theory.
The question asks what really happened: 36.7%.
Careful: not P(tails) = 50% ✗
36.7% is far from 50%.
With so few flips, that can happen.
More flips usually get closer.
= 36.7% < 50%
3 Check
Let's check: 36.7% of 30 flips should be the 11 times.
36.7% of 30 is about 11.
So the answer is right!
36.7% of 30 = 11 ≈ 11
Let's look back.
First: times it happened over times tried.
Then: compare with the theory.
Last: check.
Answer
= ≈ 36.7%