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### Unit 8: Lesson 3

Lesson 4: Estimating probabilities through repeated experiments

# Experimental probability

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. •   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.
• 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 😭) • 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.
• 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! :) • how do you change to percentage or decimal of any number • what is the difference between theoretical probability and simple probability? • 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! • 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.
• What is that symbol he draws at ? • I'm confused. Could someone explain what experimental probability is, please? Thanks! • 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?
• I dont understand this.. its very confusing to me • 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:) 