eli5 If an unbiased coin has a 50% chance of getting heads and 50% of getting tails. If you roll 10 times why is it unlikely for you to get 5 heads and 5 tails. From a probability standpoint, shouldn’t you guarantee that?

Question

eli5 If an unbiased coin has a 50% chance of getting heads and 50% of getting tails. If you roll 10 times why is it unlikely for you to get 5 heads and 5 tails. From a probability standpoint, shouldn’t you guarantee that?

In: Mathematics

Answer 1

The 50 percent probability is a *theoretical* probability. Since there are two possible outcomes – heads or tails – then you theoretically have a probability of getting heads or tails half the time.

But theoretical is not reality. If you run the experiment ten times, you’re likely to have a different result – maybe heads 7 times and tails 3 times.

There’s a rule of large numbers which states that the more times you run the experiment, the closer you get to that theoretical probability though. So if you flip a coin 10 times and get 70/30, then flip it 100 times you might get 60/40, and then flip it 1,000 times and you’ll see it come out to 53/47, and then flip it 10,000 times and it’ll be closer to 50.01/49.99