Suppose two dice are thrown 1000 times and a seven (sum of the dots) occurs 312 times.
a. What is the empirical probability of a seven occurring with these dice?
b. What is the calculated probability of a seven occurring with these (or any) dice?
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The answer is basically about 312 times per 1000.....all numbers will come out depending on the luck of the throw.....it may come out 100 times on the next 1000 throws.....it's not easy to put a %age on this.
Empirical probability is the probability determined from actual data that you've gathered. So for this case, it would be 0.312.
The calculated probability is determined from probability theory. Simply put, how many ways are there to roll a seven?
Die 1 Die 2
1 6
2 5
3 4
4 3
5 2
6 1
So there are 6 ways to roll a 7. If you're rolling two dice, the total number of permutations you can have is 6 x 6 = 36. So the calculated probability is 6 / 36 = 0.167.