![]() The probability that I picked out a fair coin, given that I Is I put my hand in the bag, and my eyes are closed,Īnd I picked out a coin. Right? Because it's going toĮither be heads or tails. Let's say that there is an 80% chance of getting a heads forĪny one of those coins, and that there is a 20%Ĭhance of getting tails. And a fair coin, of course, isĪ 50:50 chance of getting heads or tails, and the unfair coin. And in that bag, I haveĥ fair coins, and I have 10 unfair coins. Probability and combinations and conditional probability. Involves almost everything we've learned so far about Sal has a whole bunch of videos on the Binomial distribution in a later section. This formula is known as the Probability Mass Function of the Binomial Distribution. That is why Sal switched formulas to use one which is based on the multiplication rule of probability, so he could multiply the 20% in for all the tails outcomes (80%^4 heads outcomes, and 20%^2 tails outcomes). ![]() If you tried a proportion with the unfair coin you would get a probability which doesn't take into account the 30% advantage that heads has. In the case of the unfair coin with heads at 80%, the proportion won't work because the outcomes are not equally likely. Because they are equally likely, the probability can be calculated by simply using a proportion - the combinations 4 out of 6 proportional to the total number of possible EQUALLY LIKELY outcomes. ![]() ![]() In the case of the fair coin, the probability of each outcome is equal at 0.5 for heads and 0.5 for tails. Great question - I see how that could be confusing.
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