Question

Flip a coin 10 times and record the observed number of heads and tails. For example, with 10 flips one might get 6 heads and 4 tails. Now, flip the coin another 20 times (so 30 times in total) and again, record the observed number of heads and tails. Finally, flip the coin another 70 times (so 100 times in total) and record your results again.

We would expect that the distribution of heads and tails to be 50/50. How far away from 50/50 are you for each of your three samples? Reflect upon why might this happen?

Detailed written explanation needed

Answer 1

number of tosses	Heads	Tails	P(Head)	P(Tail)
10	6	4	0.6	0.4
30	17	13	0.566667	0.433333
100	52	48	0.52	0.48

The table above is an example of relative frequency estimate of a probability.

Assuming that the coin is fair, heads and tails are equally likely in ideal case
Required probability = Number of outcomes in the event ÷ Total number of possible outcomes

For the coin, number of outcomes to get heads = 1
Total number of possible outcomes = 2 (heads and tails)
Thus, required probability = 1/2

This, result will come when sample size (number of tosses) is very large quantity