Say you have a coin and, if flipped, will land either heads or tails. What is the probability that it lands, say, heads? The "real" answer is that the probability is unknown. The information was not given at the start. We cannot proceed further then. But if we insist on moving on, we have to have a number. So we *assume* the probability is *exactly* 1/2 because there is one desired outcome (heads) and there are two possible outcomes (heads, tails). Because no information is given, we have no reason to think that heads are more likely or that tails are more likely.
Say an urn C has exactly one ball, either a red ball or a white ball. That's the only information you have. What then is the probability that a, say, red ball is drawn? The *real* answer is that the probability is unknown. But if we insist on moving on, we *assume* the probability is *exactly* 1/2.
Urn B has only red or white balls. We don't know how many of each there are. What is the probability that, say, a red ball is drawn? We *assume* the probability is *exactly* 1/2. This is the same as the probability for urn A. And since the probabilities are the same for urn A and for urn B, there is no reason to prefer one over the other.
JRN
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2021-06-30T14:34:35Z (over 3 years ago)