Question

Use the DeMoivre-Laplace limit theorem to approximate the probability of getting heads exactly 50 times in 100 tosses of a fair coin.

Answer 1

We want to know the probability of getting exactly 50 heads.

First, realize that from the 100 positions, you can count how many ways there are to get 50 heads. Since they can be in 50 positions, there are (¹⁰⁰C₅₀) ways of arranging 100 coins with exactly 50 heads.

Now we need the total number of possible coin flips. Each flip has 2 possibilities and there are 100 flips, so there are 2¹⁰⁰ possible flips.

Thus, the probably of flipping exactly 50 heads out of 100 = ¹⁰⁰C₅₀/2¹⁰⁰

= 7.96%