Main content

## 7th grade (Illustrative Mathematics)

### Unit 8: Lesson 3

Lesson 4: Estimating probabilities through repeated experiments# Experimental probability

CCSS.Math:

Based on past experience, we can make reasonable estimates of the likelihood of future events.

## Want to join the conversation?

- I still don't really understand what experimental probability is.(15 votes)
- Experimental probability is the actual result of an experiment, which may be different from the theoretical probability.

Example: you conduct an experiment where you flip a coin 100 times. The theoretical probability is 50% heads, 50% tails. The actual outcome of your experiment may be 47 heads, 53 tails. So the experimental probability of getting tails in 100 trials is 53%, and 47 for getting heads in 100 trials.(78 votes)

- I'm still confused. I've come across many problems which tells me to convert to experimental probability, and I still don't know how to.

For example: *What is the theoretical probability of rolling an even number on a 6 sided dice? What would be the experimental probability?*

Honestly, I'm really confused.....I know the theoretical probability on the easy sample problem I said above is 1/2, but I don't know the answer for the expiremental probability.

(I have a math test tomorrow, plz help 😭)(11 votes)- From what you wrote, there isn’t enough information to find the experimental probability of an even number, because this probability depends on the results of an experiment. You would need to know the number of rolls and the number of even numbers that came up out of these rolls. For example, if you were told that 6 even numbers came up out of 10 rolls, the experimental probability of an even number would be 6/10, or 3/5.(9 votes)

- I know a lot of people have been struggling with this area of the unit, so here is a much more understandable version of Sal's Lesson:

Difference between Theoretical and Experimental:

While Theoretical is exact, Experimental is an 'educated guess'.

Ex-

I played 16 games so far. For my 17th game, I want to know what the probability of scoring greater than or equal to 30 is.

P(Pts greater than or = 30)

Using theoretical I cannot solve this because it does not have the correct data. But, If I was using the experimental method, I could use this info from my last 16 games to create a close enough guess.

In my last 16 games, I gather that in only 5 of my games, I scored more than or equal to 30 pts.

Therefore,

P(Pts greater than or = 30) = 5/16 (IN THE PAST - 'An indicator of what might be')

Experimental - Based on Experience

Feel free to point out anything if I got it wrong...

HOPE THIS HELPS! :)(16 votes) - how do you change to percentage or decimal of any number(5 votes)
- you divide the numerator by the denominator of the fraction form of the probabilitie(8 votes)

- what is the difference between theoretical probability and simple probability?(7 votes)
- Well, Cole, theoretical probability is what
*should*happen. However, I am still puzzled about what you mean by simple probability.(4 votes)

- What is that symbol he draws at1:13?(0 votes)
- ≥ means greater than or equal to.

≤ means less than or equal to.

> means greater than,and

< means less than.

If you want more information you could research about it.(8 votes)

- I'm confused. Could someone explain what experimental probability is, please? Thanks!(6 votes)
- It is distinguished from theoretical probability and is like it sounds, you do an experiment to see what happens.

So if you roll a number cube six times, theoretically you would get each number 1-6 once. However, if you try an experiment (get a number cube, roll it and record what you get and do this six times) you may get each number once, but you are more likely going to have one or more number repeat. If you do it 100 times or 1000 times, you should get closer to each number being rolled about the same number of times. Does this make sense?(2 votes)

- I dont understand this.. its very confusing to me(3 votes)
- How to find experimental probability of certain even?

Conduct an experiment and record the number of times the event occurs and the # of times the activity is performed then divide the two numbers to obtain the Experimental Probability.

Example: A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

well, you actually conduct an experiment:

-Take a marble from the bag.

-Record the color and put back the marble in bag.

- Repeat a few times (maybe 50 times).

Count the number of times a blue marble was picked

Suppose it is 13.

experimental p(getting a blue marble) = 13/50

if you find it using theoretical probability then it would be approx. 8/20 = 2/5

Hope that helps:)(5 votes)

- i have no clue i watched every vid and tried it and dont understand(6 votes)
- Say you have the experimental probability of 16/30 what you wanna do is divide 16 by 30.(1 vote)

- Can somebody please tell me what a favourable outcome is? I can't seem to find any help on it and i need it to solve questions!(3 votes)
- It's an outcome that meets the experiment's criteria.

For example, let's say we roll a dice. We want to know the possibility of rolling an even number. There are three even numbers: 2, 3 and 6. Rolling an even number is a favourable outcome.

3 (favourable outcomes) / 6 (possible outcomes) gives us a 50% chance of rolling an even number.

"What is the possibility of picking a blue marble from a bag of 7 blue marbles, 3 green marbles and 9 red marbles?" The number of favourable outcomes here would be 7, because there are 7 blue marbles in the bag.(2 votes)

## Video transcript

- [Voiceover] There's a
lot of times, there's a lot of situations in which
we're studying something pretty straightforward and we can find an exact theoretical probability. So what am I talking about? Just let me write that down. Theoretical probabiity. Well, maybe the simplest example, or one of the simplest examples is
if you're flipping a coin. And let's say in theory you're flipping a completely fair coin and you're flipping it in a way
that is completely fair. Well, there you know
you have two outcomes. Either heads will be on top
or tails will be on top. So theoretically you say, "well, look, "if I want to figure out the probability "of getting a heads, in theory I have two "equally likely possibilities, and heads "is one of those two equally
likely possibilities." So you have a 1/2 probability. Once again, if in theory the coin is definitely fair, it's a
fair coin and it's flipped in a very fair way, then this is true. You have a 1/2 probability. We could also do that with rolling a die. A fair six-sided die is
going to have six possible outcomes: one, two,
three, four, five and six. And if you said "what is
the probability of getting "a result that is greater
than or equal to three?" Well, we have six equally
likely possibilities. You see them there. In theory, if they're all equally likely, four of these possibilities
meet our constraint of being greater than or equal to three. We have four out of the six of these possibilities meet our constraints. So we have a 2/3, 4/6 is the same thing as 2/3, probability of it happening. Now these are for simple things, like die or flipping a coin. And if you have fancy computers or spreadsheets you can even say "hey, "I'm gonna flip a coin a bunch of times "and do all the
combinatorics" and all that. But there are things that are even beyond what a computer can find the exact theoretical probability for. Let's say you are playing a game, say football, American football, and you wanted to figure
out the probability of scoring a certain number of points. Well that isn't very
simple because that's going to involve what human beings are doing. Minds are very unpredictable, how people will respond to things. The weather might get involved. Someone might fall sick. The ball might be wet,
or just how the ball might interact with some player's jersey. Who knows what might actually result in the score being one point this way, or seven points this way,
or seven points that way. So for situations like
that, it makes more sense to think more in terms of
experimental probability. In experimental probability,
we're really just trying to get an estimate of something happening, based on data and experience
that we've had in the past. For example, let's say you had data from your football team and it's
many games into the season. You've been tabulating
the number of points, you have a histogram
of the number of games that scored between zero and nine points. You had two games that scored between zero and nine points. Four games that scored
from ten to 19 points. You had five games that
went from 20 to 29 points. You had three games that
went from 30 to 39 points. Then you had two games that
go from 40 to 49 points. Now let's say for your
next game, let's see how many games you've had so far. The game so far is two plus four plus five plus three plus two, so this is six, plus five is 11. Eleven plus five is 16. So you've had 16 games so far this season and you're curious, for your 17th game, you want to figure out,
what is the probability your points are greater
than or equal to 30? The probability your
points are greater than or equal to 30 for game 17. Once again, this is very hard to find the exact theoretical probability. You don't know exactly, you
can't predict the future. You don't know who's gonna show up sick, how humans are going to
interact with each other. Maybe someone screams
something in the stand that just phases the quarterback in exactly the right or the wrong way. You don't know. This is an incredibly, incredibly complex system, what might happen over the course of an entire football game. But you can estimate what'll happen based on what you've seen in
your past experience. It depends on the defense of the team you're facing and all that. So it's not going to be super exact, but you could estimate,
based on experiments, based on what you've seen in the past. Here, the experimental probability, and I would say the estimate, because you shouldn't walk away saying, "okay, we absolutely know for sure "that if we conducted this next game "experiment n times that it's definitely "gonna turn out the same." Because this might be the toughest defense that you play all year, this might be the easiest defense
that you play all year. But if you look at what's happened in the past, out of the 16 games so far, there have been three games, these three plus these two games, where you scored greater than or equal to 30 points. So five out of the 16 situations, you've scored more than that. An estimate of your probability, you could view this as maybe your
experimental probability, of scoring more than
30 points based on past experience, based on
past experience, is five, five out of the 16 games
you've done this in the past. So you'd say it's 5/16. Now I want to really have you take this with a grain of salt. You should not say "okay, I know for sure "there's a 5/16 probability
of us winning this game." Because you only have some data points, every team you play is
going to be different, it's going to be different
weather conditions, people are going to be in
different moods, etc., etc. This is really just an estimate. I feel a little bit of reservations even calling it a probability. I would just say that this has been true of five out of 16 games in the past. So it's an indicator of what might be. You might say, "okay, based
on experience, it's more "likely than not that we don't
score more than 30 points." But it's really just based
on experiential data, what's happened in the season. Even the makeup of your football team might have changed. You might have gotten a different coach, you might have learned to train better. Who knows, one of your team members might have grown by three inches. All of these things. So all of this has to be
taken with a grain of salt. But this is one way of thinking about it. At least having a sense
of what may happen.