A die is rolled 50 times and 1 comes up 10 times, find the…

Step by step, with the reason for every step · Experimental probability · Probability

Step by step

Question: A die is rolled 50 times and 1 comes up 10 times.

Find the experimental probability of rolling a 1.

It happened 10 times out of 50 rolls.

So the experimental probability is 10/50.

P(a 1) = 1050

Experimental probability comes from what really happened in the experiment.

experimental = what really happened

10 and 50 can both be divided by 10.

So it is 1/5.

= 10 ÷ 1050 ÷ 10 = 15

As a percent: 5 times 20 is 100.

1 times 20 is 20.

So it is 20%.

= 1 × 205 × 20 = 20100 = 20%

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: 20%.

Careful: not P(a 1) = 16.7% ✗

20% is close to 16.7%.

With more rolls, it usually gets even closer.

= 20% > 16.7%

Let's check: 20% of 50 rolls should be the 10 times.

20% of 50 is 10.

So the answer is right!

20% of 50 = 10

Let's look back.

First: times it happened over times tried.

Then: compare with the theory.

Last: check.

Answer

= 1 × 205 × 20 = 20100 = 20%

Try this one yourself, then check:

Show the answer

20%