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 odds of an event are altered for things that have already happened. What are the odds that the last eight roulette spins were black? If you weren’t watching, you might say they were less than 1%. If you did watch the last eight spins and they *were* all black, it doesn’t matter what the chances are normally: the chance of it having happened changes to 100%.
Let’s say you enter a lottery where your chance of winning is one in a million, and then you toss a coin where the chance of you winning is one in two.
The odds of you winning the lottery *and* winning the coin toss is one in two million.
But: if you already won the lottery, the chances of you completing the “win the lottery then win a coin toss” game changes, because we’ve established that you did the hard part already. So at that point the odds of you winning the lottery and winning the coin toss are now one in two.
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