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Conditional Probability
Conditional probability is the art of updating probabilities based on given information. What is the probability that the sidewalk is wet? And what if we know that it rained a few hours ago?
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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Which of the following equalities is not necessarily true if \(A, B\) are events?
Excel in math and science
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Suppose you flip a fair coin 10 times. What is the probability of the last two flips both being heads if you know that the first eight flips were heads?
Excel in math and science
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Our wiki is made for math and science
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\[ P(A \mid B) = P(B \mid A).\]
which of the following must be true of \( A \) and \( B, \) if \(P(A \cap B) > 0?\)
Excel in math and science
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Suppose there are two types of surgeries that doctors perform. Doctor A has a higher success rate than Doctor B on the first type of surgery. Doctor A also has a higher success rate than Doctor B on the second type of surgery. Is it true that Doctor A necessarily has a higher overall success rate than Doctor B?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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Used and loved by 4 million people
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Assume that a child has an equal chance of being born on any month and of either gender (male, female). Let \( p \) be the probability that given that a family has two children and at least one of them is a girl, both are girls. Furthermore, let \( q \) be the probability that given that a family has two children and at least one of them is a girl born in April, that both are girls. Does \( p = q \)?