Some intuitive reasoning
If A is a subset of B and B' isn't equal to 0, is P(A) larger or smaller than P(A|B)? Provide some intuitive reasoning for your answer.
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Suppose we roll three fair six-sided dice. Compute the conditional probability that the first die shows 4, given that the sum of the three numbers showing is 12.
A dreidel is a four-sided top that contains a Hebrew letter on each side: nun, gimmel, heh, shin. Here we suppose that a fair dreidel is to be spun ten times. Compute the probability of each of the following events:
Suppose that births are equally likely to be on any day. What is the probability that somebody chosen at random has a ba birthday on the first day of a month? How does this probability change conditional on the knowledge that the person's birthda
The standard deviation for using a certain radar detector is .68 mph for vehicle speeds around 45 mph. If you were traveling 42 mph in a 30 mph zone and if a police officer used his speed detector, what is the probability that you will be clocked
In a certain city 30% of the people are Conservatives, 50% are Liberals, and 20% are Independents. In a given election, 2/3 of the Conservatives voted, 80% of the Liberals voted, and 50% of the Independents voted. If we pick a voter at random what
Suppose you have 22 shoes in a basket: 5 identical pairs of sneakers, 4 identical pairs of sandals, and 2 identical pairs of dress shoes. You select shoes from the basket in the dark, hoping to get a matching pair, and can check them only after a
The standard deviation for using a certain radar speed detector is 0.68 mph for vehicle speeds around 45 mph. If you were traveling 42 mph in a 30 mph zone and if a police officer used this speed detector, what is the probability that you would be
The crew of the Starship Enterprise is considering launching a surprise attack against the Borg in a neutral quadrant. Possible interference by the Klingons, though, is causing Captain Picard and Data to reassess their strategy.
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