I know, 50/50 heads tails right? But help me understand the next step – each coin flip has a 50/50 shot of heads or tails. What I don’t understand is how the likelihood of the next flip doesn’t change. For example if I flipped a coin 10 times and every time it flipped heads, the next flip would be 50/50 tails. Wouldn’t the likelihood of flipping a coin 11 times and having it be heads every time be really low? 0.5^11 = 0.048%?
Here’s the origin of the question. I was at a roulette table and the guy said “it’s been black the last 8 rolls, the next one has to be red.” At first I thought, the next roll will be ~47% black, ~47 red, ~6% 0 or 00 you fucking imbecile. Then I thought to myself, what are the chances that there are no red rolls in 9 rolls, which is well below 1%.
Am I the imbecile?
In: 215
The best way to think about this (IMHO) is as follows:
The chance of getting heads (or tails) from a fair coin is 50% or 1 in 2. This means that, if we flip a coin a lot of times, chances are (close to) half of the flips will be heads, and (close to) half will be tails.
When we say the chances of 4 heads in a row is 1/16 (1/2 for the first, 1/4 for 2 in a row, 1/8 for 3 in a row, and 1/16 in a row), what we are saying is: if we flip a coin ___4 times a lot of times___, that is to say, we perform a series of 4 flips over and over, (close to) 1/16 of those series will be all heads.
Each individual coin flip is ignorant of every other, and whatever happened before doesn’t matter: the next coin always has a 50:50 chance of being heads or tails.
Latest Answers