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Unformatted text preview: p and tails with probability q = 1p . We toss the coin n times. What is the probability that the number of heads and the number of tails are equal? 4. Let A and B be events with probabilities P ( A ) = 3 / 4 and P ( B ) = 1 / 3. ind the smallest and the largest possible values of P ( A B ) and of P ( A B ). 5. Let A 1 and A 2 be events. Prove that P ( A 1 A 2 ) P ( A 1 ) + P ( A 2 )1. Prove that in general P ( A 1 . . . A n ) n s i =1 P ( A i )( n1) for events A 1 , . . . , A n in a probability space. 1...
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 Winter '12
 AlexanderBarvinok
 Probability

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