Question

does a simulation using randomly generator numbers give theoretical or experimental propablilities? explain.

Answer 1

Simulation using random numbers will give experimental probability which would be nearing the theoretical probability for large sample of random numbers.

For instance,

1) the theoretical probability of head in each toss of coin in .50.

2) If we conduct a experiment by randomly generating number between 1 and 100 and if number comes out to be less than or equal to 50, we classify it as head or else as tail.

3) If we conduct experiment only 2 times, it's possible we end up getting number less than 50 in both the experiments and hence, classify it as head which would result in experimental probability of 1.

4) But if we keep on running the experiment for, let's say, 10000 trials, it will converge very near to the theoretical probability of 0.50.