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Results tagged with probability
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user 42028
A probability expresses quantitatively how likely an event is to occur. We often encounter probabilities as conditional probabilities which express how likely an event is to occur in light of certain (given) information.
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two guys flip fair coins until they obtain their first heads. it takes strictly fewer flips ...
First, we calculate the probability $ P(X < Y) $. … Using the law of total expectation, conditioned on $ X < Y $:
$
E[X \mid X < Y] = \sum_{k=1}^\infty k \cdot P(X = k \mid X < Y)
$
The conditional probability $ P(X = k \mid X < Y) $ is
$
P(X = k \mid X …
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