Introduce another one that's more helpful when we can't thinkĪbout equally likely events. Here because this was just one way of thinking So once again, you have aġ/2 chance of that happening. You said the probability of getting an even numberĮqually likely events, and there's three even
Of a fair coin, the probability of heads-Įqually likely events, and we're saying one of And this is all of theĮqually likely events. Number of events that satisfy A over all of theĮqually likely events. That was the probability of A occurring is the With one way of thinking about probability, and (ie) P(HHHHHHHHHH) as well as P(HHHHHHHHHT) or even P(HTHTHHTTHT) is the same 1/512. If you see the sample space, the probability of any combination of tails and heads for ten times is 1/512.
The probability for the tenth throw in a row does NOT assume correlated events. "But calculating the probability for the tenth throw in a row assumes the same thing, correlated events" (ie), the most unlikely event component of the very small probability has already occured.
Now, to get past this paradox, instead of thinking that the probability of getting all heads 6 times is very less(1/64 to be exact) and it's likely to be a tail the sixth time, we must think that we've already gotten 5 heads in a row, the probability of which is 1/32 and irrespective of the sixth try being a tails or a heads, the probability will be 1/64. Now, the paradox for the sixth try is betweenĪ) that we tend to believe that it is more likely to get a tails now as we've got a series of heads already and because the probability of getting an all heads in a row is always lessī) the probability for each event remains the same (Gambler's fallacy) Let's assume that we've tossed a fair coin five times already and that all were heads.
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