Probabilty w/ dice: using data from my 100 rolls

[Btoepp]

This should be the easiest part to understand, but i'm confused:

Use the data from your 100 rolls to estimate the probability of getting each possible numeric value. Repeat the process after combining your data with the data of your partner (you will get your partner’s data in class on the 5th or 6th).

does this mean it would look something like this

Rolled six 10's out of 100 rolls

Chance of rolling a 10 is 6/100?

 

[Mrspi]

Re: Probabilty w/ dice

This should be the easiest part to understand, but i'm confused:
Use the data from your 100 rolls to estimate the probability of getting each possible numeric value. Repeat the process after combining your data with the data of your partner (you will get your partner’s data in class on the 5th or 6th).

does this mean it would look something like this

Rolled six 10's out of 100 rolls

Chance of rolling a 10 is 6/100?

Yes....that's exactly what it means. This is the "experimental probability" obtained in your experiment of rolling the dice 100 times. It may or may not be the same as the "theoretical probability" you could calculate by knowing that there are 36 possible ways for two dice to land, and of those, 5 have a sum of 10 on the faces of the dice. The theoretical probability of rolling a sum of 10 with two dice is 5/36.

 

[Btoepp]

Re: Probabilty w/ dice

[Yes....that's exactly what it means. This is the "experimental probability" obtained in your experiment of rolling the dice 100 times. It may or may not be the same as the "theoretical probability" you could calculate by knowing that there are 36 possible ways for two dice to land, and of those, 5 have a sum of 10 on the faces of the dice. The theoretical probability of rolling a sum of 10 with two dice is 5/36.

That was a great help! so again, using the 2 dice example, if i rolled eight sixes the theoretical probability of me rolling a six would be 8/36 or 2/9? And how do you find out how many ways two dice can land. I want to say you just added another 12 on there, so i would do the same for 3 and add another 12 to it to make it 48, but I'm probably wrong.

 

[Mrspi]

Re: Probabilty w/ dice

If you roll two dice, here are the possibilities of what you can get....


1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4, 6-5, 6-6

If you count those, you'll see that there are 36 possible outcomes when you roll two dice.

Let's say you are looking for the "theoretical probability" of rolling an 8....

You can get an 8 on a roll of two dice with 6-2, 2-6, 5-3, 3-5, or 4-4

So...there are 5 ways to get a total of 8 on the two dice. So, the theoretical probability of getting an 8 on a roll of 2 dice is 5 out of 36 possibilities, or 5/36.

If you actually perform an experiment, where you roll two dice a number of times, say 100 times, you'd count the number of times a sum of 8 comes up. The "experimental probability" of rolling an 8 would be the number of 8's you actually got, divided by the number of rolls you made (100 in our example).

While "theory" tells us that the probability of getting an 8 is 5/36, and you might expect that 5/36 of your 100 rolls should produce a sum of 8, that may not (and PROBABLY won't) be what happens.

In your experiment of rolling two dice 100 times, the number of times that a total of 8 comes up may be more or less than the (5/36) * 100 that theoretical probability would predict.