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ie was rolled twice. The first time it landed on a number that we will call “x”. The second time it landed on a number that we will call “y”. We will symbolize some events as follows: A: x is odd. B: x is a prime. C: y is odd. D: y is a prime. Express the following probabilities using the notation “p(. . . )”. For example, the chance that x and y are both odd may be expressed as p(A ∧ C). (1) The chance that x is odd and y is even. (2) The chance that x and y are not both odd (i.e., at least one is even). (3) The chance that x is a prime given that it is even. (4) The chance that x is even given that it is a prime. (5) The chance that x and y are both primes given that they are both odd. (6) The chance that at least one of x and y is a prime given that at least one of them is odd.
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