what is relationship between experimental probabilities, theoretical probavililties, and the number of trials.

Question

And Why!
A, Experimental probabilities approach theoretical probabilites as the number of trials incareases

B, Theoretical probabilities approach experimental probabilites as the number of truals decreases.

C, Experimental probabilities appproach theoretical probabilities as the number of trials decreases.

D, nome of the above

Answer 1

Experimental probability is obtained by carrying out some trials to see what fraction of the time the event you are looking for occurs. For example, if you want to know the probability of scoring a total of 8 when you throw a pair of dice, one way of doing it would be to throw a pair of dice five times and see how many times you get 8. If it happened twice, you would say the experimental probability is
2/5, or 0.4
Not a very good result, though, too few trials. If you did it 100 times, and 8 showed up 15 of those times, the experimental probability would be
15/100, or 0.15

Theoretical probability is found by considering how many equally likely outcomes there are, and in how many of those outcomes the event you are looking for occurs. In the example I just gave, there are 36 different ways for the dice to land, and the total is 8 in 5 of those ways, so the theoretical probability is
5/36, or 0.13888...

We expect a very small number of trials will not give a very good picture of the real probability. Choose your answer from that.

Answer 2

Theoretical Probabilities

Answer 3

A. Think about rolling a single dice. The theoretical probability is 1/6 to roll a 3. Experimentally, I roll the dice twice. There is no way I will get 1/6 of my rolls to be a 3. I have to make lots of rolls of the dice before the experimental probability (i.e. what I get when I actually roll the dice) gets close to the theoretical probability. If I have rolled the dice 600 times probably I'll have close to 100 3's come up, but even then probably not exactly. But the more times I roll the dice, the closer I will come to that theoretical number of 1/6 of the rolls being a 3.