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Problem regarding the de morgan

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Reference no: EM13845118

Problem 1: We shall prove in class next time that An ↑ A implies limn→∞ P(An) = P(A). Use this fact to prove that An ↓ A implies limn→∞ P(An) = P(A). [Hint: De Morgan might be of help.]

Problem 2: For any sets A, B, C, prove that

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(C ∩ A) + P(A ∩ B ∩ C)

If the events A, B, C are independent, show that the above expression can be simplified to

P(A ∪ B ∪ C) = 1 - [1 - P(A)][1 - P(B)][1 - P(C)].

Problem 3: Suppose I have a biased coin with probability of H = 0.25. I make 5 independent flips of that coin. What is the probability that I see more heads than tails?

Problem 4: Suppose A and B are two independent events. Show that (i) A and Bc are independent, (ii) Ac and Bc are independent.

Verified Expert

This assignment has been prepared in word where all the three question are answered, now it is based on calculation of conditional and unconditional probability including the independent events. It also includes the binomial distribution calculations. The work is fully original and there is no plagiarism.

Reference no: EM13845118

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