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Answer the following short questions. Show all your work where possible (if the answer is incorrect, part marks will be based on work shown).
(a) Suppose that the probability of living to be older than 70 is .6 and the probability of living to be older than 80 is .2. If a person reaches her 70th birthday, what is the probability that she will live beyond her 80th birthday?
(b) Is it true in general that P(A)P(A n B) s (P(A))2. Explain your answer carefully.
(c) In an experiment with two independent fair coin tosses, let A be the event of observing two heads and let B be the event of observing two tails. Are the events A and B independent? Justify your answer using probability. [I-Iint: write out full the sample space to ?nd the required probabilities]
(d) In an experiment with two independent fair coin tosses, let A be the event of observing heads on the ?rst toss and let B be the event of observing heads on second toss. Are the events A and B independent? Justify your answer using probability. [I-Iint: write out full the sample space to ?nd the required probabilities]
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