# What is the probability of of 32 coins landing on heads if 100 coins are flipped?

Exactly 32

### 4 Answers

- PuzzlingLv 71 year agoFavorite Answer
I'll assume you want the probability of exactly 32 heads.

Use the binomial probability formula:

P(X = k) = C(n,k) * p^k * q^(n-k)

n : number of trials (100)

k : number of successes (32)

p : probability of success (1/2)

q : probability of failure (1/2)

P(X = 32) = C(100,32) * (1/2)^32 * (1/2)^68

= 100!/(32!68!) * (1/2)^100

= 143012501349174257560226775 / 1267650600228229401496703205376

≈ 0.000113

≈ 0.0113%

Answer:

About 0.0113%

- King LeoLv 71 year ago
.

Binomial

P(X = k) = C(n, k) p^k q^(n - k)

p = probability of a success = ½

q = probability of a failure = ½

n = number of tosses = 100

k = exact number of heads required = 32

P(X = 32)

= C(100, 32) (½)³² (½)⁶⁸

= C(100, 32) (½)¹⁰⁰

= 100! / (68! 32! ) (½)¹⁰⁰

= 143012501349174257560226775 / 1267650600228229401496703205376

- 1 year ago
pretty likely I'd say. tossing a coin is a 50-50 chance but that's not always the case. out of a large number its possible to get other percentages. I'm pretty sure.

If that isn't clear, just imagine what would happen if you calculated P(100,32) instead. You'd get a result that was much greater than 1 which isn't possible for a probability.