Question

Did I answer this correctly? I recorded the sum of the dice rolls. The Theoretical Probability goes all the way to 12.

Find the experimental (as you experienced) probability of rolling each sum. Fill out the following table: Probability of occurrence for each sum out of our 72 total rolls (record your probabilities to um of the dice Number of times each sum occurred hree decimal places) 2 2 0.028 6 0.833 0.069 0.153 10 0.139 0.125 7 0.097 8 10 3 0.142 9 0.125 12 2 0.028

Answer 1

First of all, I think you have made a typo in the observed section probability.

For the sum value 2, the observed frequency = 6. And total number of observation = 72

So, the required probability = 2/72 = 0.0833

I think you have made a typo and missed a decimal there.

And then for sum value of 10, the observed frequency is 3 and the total number of observations = 72.

So, the required probability should have been = 3/72 = 0.042

But I think you have made a calculation mistake. You divided 10 by 72 instead of dividing 3 by 72.

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Now, coming to the theoretical probabilities.

You need to understand that when you roll a pair of dice, the total number of possible outcomes = 6 x 6 = 36.

And those 36 possible outcomes along with their sum are listed below -

What you have done is that you have put the denominator as 72 in each case which should be 36 instead.

I think you got confused with the previous work you did. There we divided by 72 because we performed the experiment 72 times and recorded the data. But while doing theoretical probability, we just look for the 36 possible values.

Here is the actual value that you should fill in -

Similarly, you can fill up to 12 as -