Experimental and Theoretical Probability Part 3

This is the third part of the Experimental and Theoretical Probability Series.

In the second part of this series, we have observed in three different experiments that if two dice are rolled, it seems that the probability of getting the sums are not equal. Not only that, we have seen several consistent patterns; for example, 2 and 12 got the least number of rolls; while, 6,7, and 8 got the most.

To investigate this observation, we examine how to get a sum of 2, 12, and 6 first when we roll two dice, and then investigate other sums later.  Recall that in the first part of this series, we experimented with two dice, one colored blue and the other red.  To distinguish which number belongs to which dice, we color the numbers blue and red to denote blue and red dice. » Read more

Experimental and Theoretical Probability Part 2

This the second part of the series of posts on Experimental and Theoretical Probability.

In the first part of this series, we used a spreadsheet to simulate the rolling of dice 1000 times and automatically recorded the sums. We have observed that the sum frequencies are not evenly distributed (see Figure 1).

Figure 1

In rolling the two dice 1000 times, for example, we rolled a seven 156 times, while we only rolled a two 29 times.  Well, we want to think that this is just a coincidence, so maybe we could try it one more time. » Read more

Experimental and Theoretical Probability Part I

This the first part of the series of posts on Experimental and Theoretical Probability.

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If two standard cubical dice are rolled, one red and one blue, the possible sums ranges from 2 = (1+1) and 12 = (6+6).

Now,  are the chances of getting these 11 sums equal?  For example, is the chance of getting a sum of 2 similar to the chance of getting a sum of 5?

Let us try to roll the two dice 1000 times.  Of course, we will not do this manually.  » Read more

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