It's not just a roll of the dice (though sometimes, it feels that way).
When the forecast says that there is a 30% chance of rain, that probability is based on all the information that the meteorologists know up until that point. Weather forecasting is based on conditional probabilities. For us, the important thing to know is, if we tested positive (an observed event), what is the chance that we truly have the disease (an unobserved event). A positive test still means we might not have the disease, and testing negative might mean we have it, though hopefully with very little likelihood. When we go to the doctor to test for a disease (say tuberculosis or HIV or even, more commonly, strep throat and flu), we get a yes or no answer. Such card counting and conditional probabilities (what's the likelihood of each hand, given what I have seen) is one of the (frowned upon) strategies for trying to beat the casinos in blackjack and poker (see the movie 21 for a Hollywood version of real-life card counting in casinos). Inveterate bridge players like my dad would keep track of cards as they got exposed in the pile, for that (and the bids) provided information about the likelihoods of what hand each player had. Some more examples of where we might encounter such conditional probabilities: What we will explore is the concept of conditional probability, which is the probability of seeing some event knowing that some other event has actually occurred. That's the subject for a future post on Bayesian statistics. This post won't speak to how these probabilities are updated. After every game the team plays, these probabilities change based on whether they won or lost. From the beginning of each season, fans start trying to figure out how likely it is that their favorite team will make the playoffs. For example, the NFL season is rife with possibilities. In addition to regular probability, we often want to figure out how probability is affected by observing some event.
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