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In this lesson, you’re going to learn about the concept of experimental probability and apply it to coins, dice, a deck of cards, and even real world scenarios.

Experimental Probability

Have you ever played with a deck of cards? If not, have you ever rolled a die? Or at the very least, I’m sure you’ve flipped a coin before! All of these can apply the concept of experimental probability, which is the ratio of the number of times an outcome occurs to the total number of times the activity is performed. Let’s go over this concept using coins, decks, and dice!

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Flipping a Coin

If you flip a coin, there are two possible outcomes: heads or tails. If you flip a coin 100 times, at least theoretically, chances are that heads will appear 50 times, or half the time.

Meaning, our theoretical probability of flipping heads is ½ or 50%. But this may not occur in practice, in an actual experiment based on testing and observation.Here’s what I mean.

Take out a coin for me. I’ll wait. Okay, flip the coin 10 times, and jot down the number of times you get heads in this experiment.

I did the experiment and got heads 7 out of 10 times. In my case, what is the experimental probability that a coin flip will yield heads? 7 out of 10, or 70% of the time. Maybe my coin isn’t fair, or maybe it’s just chance alone that yielded this result. However, if we were to flip a fair coin a 1,000 times, the experimental probabilities would come closer to matching the theoretical probabilities.

Rolling a Die and Picking a Card

Now, let’s play with a die. On the screen we can see the die being rolled.

In an experiment of 10 rolls of the die, a 3 appears 4 times. What is the experimental probability of rolling a 3? It’s 4 out of 10, or 2/5, or 0.4, or 40%. What is the experimental probability of rolling any number other than a 3 in this case? Well, it’s simply a matter of subtracting 4 from 10, to get 6 out of 10, or 60%.

Let’s try another example. What if I roll the die 30 times and get the number 6 a total of 10 times? What is the experimental probability of rolling a 6, then? It’s 10 out of 30, or 1/3. Now, let’s take out a standard deck of 52 playing cards. If I replace each card after every try and reshuffle the deck after every try as well, then if out of ten tries I pull out a heart 5 times, what is the experimental probability that I will pull out a heart? It’s 5 out of 10 which is the same thing as 1/2.

0.5, and 50%.

Real World

Experimental probabilities don’t just have to deal with coins, dice, and cards only. We can apply this concept to a real world scenario.Let’s say that you’re a cashier in a store. You notice that of the 20 people that have passed through your register, 3 have bought apples.

What is the experimental probability that the next person you see will be buying apples? It’s 3 out of 20.If you are standing at an intersection, just watching the traffic go by, and you notice that out of 100 cars, 3 are yellow in color, then what is the experimental probability the next car you see will be yellow in color? 3 out of 100, or 3%.

Lesson Summary

Experimental probability is the ratio of the number of times an outcome occurs to the total number of times the activity is performed. You’ve now learned how to apply this concept to everything from coin flips to real-world scenarios.

Don’t forget that experimental probability is not the same thing as theoretical probability. They may not match!

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