Coin toss probability

Coin toss probability is explored here with simulation. Use the calculator below to try the experiment. Click on the button that says "flip coin" as many times as possible in order to calculate the probability. After you have flipped the coin so many times, you should get answers close to 0.5 for both heads and tails.  




When asked the question, what is the probability of a coin toss coming up heads, most people answer without hesitation that it is 50%, 1/2, or 0.5.

We get this probability by assuming that the coin is fair, or heads and tails are equally likely

The probability for equally likely outcomes is: 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

Thus, we get 1/2

However, if you suspect that the coin may not be fair, you can toss the coin a large number of times and count the number of heads

Suppose you flip the coin 100 and get 60 heads, then you know the best estimate to get head is 60/100 = 0.6

This way of looking at probability is called the relative frequency estimate of a probability

The interesting thing with this is that the more you flip the coin, the closer you get to 0.5

If you have a computer, you can simulate coin toss probability with different numbers of coin tosses, the result might be a table like this.

Number of tosses Number of heads Probability to get heads
4 1 0.25
100 56 0.56
1000 510 0.510
10000 4988 0.4988

Notice that for 10000 flip, the probability is close to 0.5

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