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% probability you mention is for a single event. If you’ve flipped a coin once and got Heads, you’re not guaranteed Tails on the next flip, it’s still 50% likely you’ll get Heads.

Similarly, if you’ve flipped 4H and 5T, your 10th flip still has the same 50% likelihood of being Heads or Tails.

So that said, you could find the probability for achieving 5H and 5T. It may be the most likely outcome, but it’s likely less than 50%, because you also have to account for the probability of all the other outcomes: 6/4, 7/3, 8/2, 9/1, 10/0, 4/6, 3/7, 2/8, 1/9, 0/10.