What percentage chance did you have that a roulette wheel would return you one of the possible outcomes of six different numbers? This is a very easy question, but the answer is, the probability that 6 numbers will appear is . The probability of seeing one of the numbers is . And I mean real probability: a roulette wheel can return any number between 1 and 6… not just 6 or 6 plus 1. So the probability that it’ll return me a number between 1 and 6 multiplied by each of the six possible outcomes is .
So when you have a probability of 1/6 that a random number that appears on a roulette wheel would return a number between 1 and 6 (in other words, the probability that a random number that appears has a greater than 5% chance of appearing), you can use it to predict the distribution of numbers that appeared on the wheel and the probabilities of those numbers that appeared on the wheel appearing.
So we’ll apply this method to another example of the same probability problem. Instead, we are going to solve for a random event that we want to predict, and determine our final probability. In this case, it is our outcome of one of our players picking up the last card of the deck: the last card of the deck is either . The last card is either played or . Now, we expect that there is 1 in 6 chance that one of the players will be playing . For this reason, we want to determine the probability that 1 of the next two cards that appear will be . We don’t know which of those two will be played as yet but we can use the distribution shown above to infer the probabilities. The probability of either of the outcomes is … 1/6
Therefore our final probability is … 6/6 which is 1/6 times the probability that each card of the deck is .
The probability that the remaining 3 cards will be is 1/6. Hence, it also remains a 1/6 possibility that the next card will be .
So we have derived a probability for each of the other outcomes for each random card. What is the probability that the outcome of that last card that the player picked up is of our outcome? It is … 1/6!
The last card that the player picked up is the last card in the deck, which means that our last card is of our outcome if the outcome was the last card in the deck. Note that this outcome is our outcome just as well, so now we also know that our outcome
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