Question

Use the web app Random numbers to illustrate the long run definition of probability by stimulating short term and long term results of flipping a balanced coin. keep the probability of a head at the default value of 50% and set the number of flips to generate a stimulation to 10

Answer 1

Consider a fair coin so that

The R code for simulating the tosses of a coin up to 100000 times and finding the probability of occurrence of heads is given below.

m <- 100
p <- 0.5
H <- 0

for ( i in 1:m)
{
h <- rbinom(1, 1, prob=p)
if (h == 0)
{ H <- H +1}
}
pH <- H/m
pH

The output for 100 simulation (short tem result) is

> pH
[1] 0.51

The output for 100000 simulation is (long term result)

> pH
[1] 0.5022

So we can see that the probability approaches the theoretical value as the number of simulations increases.

If you have any doubt please revert.