Why is the probability of 3 coins landing heads 1/8?

Question

The probability of a single coin landing heads is $1/2$.
Using simple probability theory, this means that the probability of three coins landing heads is $1/2*1/2*1/2=1/8$

However, if we don't enumerate or distinguish the coins, the possible end combinations we see after flipping all three coins are
TTT
TTH
THH
HHH
Since one of these four is our desired combination of three heads, the probability would seem to be $1/4$.

Why isn't this the case?

There are four possibilities, but they are not equally probable. There are three ways to get two tails and one head, while only one way to get three heads. — Jair Taylor, Jun 12 '20 at 19:57
No. OP says the coins are indistinguishable, @herb steinberg — UmbQbify, Jun 12 '20 at 20:00
The coins are distinct in reality. Thus, they need to get distinguished for a meaningful analysis. — Doug Spoonwood, Jun 12 '20 at 20:02
Tow coins are only not distinguishable if they can be at the same place at the same time. But then they are in fact one coin only. — callculus42, Jun 12 '20 at 20:05
It could be one coin flipped three times - the sequence of outcomes is what matters. — herb steinberg, Jun 12 '20 at 20:05

score 1 · Answer 1 · answered Jun 12 '20 at 19:59

1

Note that the cases TTH, THT and HTT are distinct because despite the coins are equal, the order of their toss matters (i.e. knowing that exactly 1 head drew is not enough, we must know at which toss did it happen).

answered Jun 12 '20 at 19:59

Mostafa Ayaz

31,924

Why is the probability of 3 coins landing heads 1/8?

1 Answers1