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
Imagine that instead of flipping a coin with “head” or “tails”, you flip 10 different types of coins. One is head/tails, another is black/white, another is sky/sea, another is summer/winter, etc.
You are about to flip your last coin. This coin is labeled, let’s say king/queen.
What are the odds you get either king or queen? 50/50, right?
Suddenly, a man bursts into the room. “WELL ACKTUALLY I labeled each side of your coins as “head/tails” in my head, and you got head all the time! So you’re guaranteed to get tails this time or it would be weird! Head is king, so you’re getting queen FOR SURE!”
Another breaks a window and yells “NONSENSE! I got the exact same idea and they all got head like you said, but in MY PAPER head is queen! You’re about to flip king!”
Keep in mind the coins you’re flipping only differ from the pattern on each side, and are otherwise perfectly balanced.
Who is right?
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