# Theoretical Probability and Experimental Probability

When we deal with probability, there is “theoretical probability” and we have “experimental probability”.

So, a quarterback completed so-and-so many many passes out of so0and-so many passes attempted.

But you could also say that there’s the probability that a specific quarterback completes 60 passes out of 100 attempts.

Question 1 of 5

1. One coin is tossed 10 times with these results:  HHTHT, THTHH.

Is the experimental probability for 'heads' greater or less than theoretical, and by how much?

A.
B.
C.
D.

Question 1 of 5

Question 2 of 5

2. One die is rolled six times with these results:  5,5,2,3,4,3.  How does the experiment compare with theory?

A.
B.
C.
D.

Question 2 of 5

Question 3 of 5

3. What is the most likely reason for an experimental probability to differ from theory?

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B.
C.
D.

Question 3 of 5

Question 4 of 5

4. The probability of rolling a pair of dice for a '7' is 1 in 6.  Am I guaranteed a '7' within six rolls?  Why or why not?

A.
B.
C.
D.

Question 4 of 5

Question 5 of 5

5. Half the time, actually rolling a pair of dice produces a '7', '11', or a 'double'.  How well does this agree with theory?

A.
B.
C.
D.

Question 5 of 5

Next lesson: Perimeter and Area

This transcript is provided for your convenience. So here, we’ve got the data from 3 football games. Now, we’ll be looking here at the probability so I’ll mark that as P, it is the probability of completion. So now we should be looking at the theoretical completion number and put this over the total number of pass attempts. So here, that is 60/100, an this translates to 60%. What we have here is “theoretical probability”. Now here, we’ve got the data from 3 games and here, we’ll just be looking at this probability, and we’ll be doing the same thing. Here, we’ll be taking the number of completions. Then, we’ll put it over the total number of pass attempts. So, right here, we’ve got 51 total completions over 67 total pass attempts and this translates to 0.76 which is 76%.

So here you can see that these two percentage numbers are quite different, and this now is the difference between experimental probability and theoretical probability.

When dealing with theoretical probability, we calculate just by looking at the odds of the things that will happen. So if somebody examines the ability of this quarterback and look at all his opponents, he could say something like, “Okay, the theoretical probability right here is that he will complete some 60% of all his passes.” Now, when all is said and done, you might want to look at experimental probability. This is what the quarterback factually did and that gives us a chance of 76%.

You could also take another example to look at this like rolling a dice.

Now, let’s look at what happens when you flip a coin. So the probability of the coin landing on heads when you flip it is 1/2. Now, let’s say you’ll flip your coin 6 times and 4 times, the coin lands on heads while it lands on tails twice. Well actually, these should have even, for there’s a 50% chance of the coin landing on heads. Then, the coin should have been landing on heads 3 times, and it should also have landed on tails 3 times.

So this here is the theoretical probability. Because, when we flip a coin, we have a 50/50 chance of what the coin will be landing on. we have a 50% chance the coin will be landing on heads and we have a 50% chance that it’ll be landing on tails. So when we’re flipping a coin 6 times, the theoretical probability will be that it’s landing on heads 3 times and also on tails 3 times. But here, we’re having our experimental probability. This now is what was actually happening. So now you know the difference between experimental and theoretical probability.