Eli5: If I flip a coin 10x what’s the chances that the next 10 flips will be the exact outcome of the first 10?

Question

Eli5: If I flip a coin 10x what’s the chances that the next 10 flips will be the exact outcome of the first 10?

In: Mathematics

Answer 1

Let’s say you flipped a coin 10 times and got this:

**HHHTTTHTTH**

Since each flip of a fair coin has a 0.5 probability of landing heads (H) and a 0.5 probability of landing tails (T), the probability of getting the exact same sequence again is calculated as follows:
P(HHHTTTHTTH)=P(H)×P(H)×P(H)×P(T)×P(T)×P(T)×P(H)×P(T)×P(T)×P(H)

P(HHHTTTHTTH)=(0.5)×(0.5)×(0.5)×(0.5)×(0.5)×(0.5)×(0.5)×(0.5)×(0.5)×(0.5)

P(HHHTTTHTTH)=(0.5)^10

P(HHHTTTHTTH)=0.0009765625
P(HHHTTTHTTH)~=0.1%