Unformatted text preview: p and tails with probability q = 1-p . 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 )-( n-1) for events A 1 , . . . , A n in a probability space. 1...
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- Winter '12
- Probability, Probability theory, Prime number, Probability space