Question

A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.

Answer 1

Hi there! Which part of the question are you stuck on? :) Have you tried anything so far?

Answer 2

no i get confused a lot so when i get confused its hard for me to understand it

Answer 3

No problem. Let's start at the beginning then. We have a number cube, so I'm assuming its labeled 1 through 6 like a dice.

Answer 4

yea

Answer 5

Do you know the formula for calculating probability?

Answer 6

no

Answer 7

\[Probability = \frac{outcome}{total}\]

Answer 8

This measures the chance of something happening. For example, if you flip a coin, you have a 1/2 chance of getting heads. There is 1 head outcome, and 2 possibilities total.

Answer 9

ok

Answer 10

For this problem, there are 6 possibilities total (the 6 numbers on the dice), but only 1 of them is a "3". So, the "theoretical probability" of getting a "3" is

1 outcome / 6 total = 1/6

Answer 11

Does that make sense? Any questions on that part?

Answer 12

yes it makes sence :)

Answer 13

Great! Alright, so what you might think after calculating 1/6 as the probability is that when you roll a dice, you should see a "3" EXACTLY 1/6 of the time. For example, if you roll a dice 60 times, you would expect to see 1/6 * 60 = 10 rolls with a "3"

Answer 14

That is only a guess based on "theory" though. Of course, we might get more or fewer "3"s when we actually perform the experiment.

Answer 15

Okay

Answer 16

So, we already answered part a. 1/6

For part b, we are going to see what the actual results from the experiment were.

Answer 17

We rolled the dice 450 times (glad I wasn't there). How many "3"s does the question say we saw?

Answer 18

uh im not sure

Answer 19

Well, if I'm reading it right it looks like they said the 3 came up 67 times. See where I'm getting that?

Answer 20

yes

Answer 21

Cool! So, now we can calculate the "experimental probability." This is just the fraction of how many we saw, divided by how many times we did the experiment. That's a very confusing way of just saying:

experimental probability = 67 / 450

Answer 22

They want us to simplify the fraction, so we could do the busy work and get...

Answer 23

well, it looks like it doesn't simplify... who knew?

Answer 24

lol yea

Answer 25

Alright, then we have part b. 67/450. Let me compare the two decimal answers real quick, just so that you can "feel' the answers better.

Answer 26

ok

Answer 27

Theory: 1/6 = .167
Experiment: 67/450 = .149

Answer 28

As you can see, the experiment is close to the theory, but not exactly the same. This will usually happen in real life. It is very rare for the experiment to perfectly match the theory. But it does a pretty good job!

Answer 29

Welp, that's the end of that. Anything you'd like me to clarify?

Answer 30

No but thank you for the help :)

Answer 31

You're welcome! Good luck with your studies.