Paper 2, Section II, 9F

Probability | Part IA, 2014

State the axioms of probability.

State and prove Boole's inequality.

Suppose you toss a sequence of coins, the ii-th of which comes up heads with probability pip_{i}, where i=1pi<\sum_{i=1}^{\infty} p_{i}<\infty. Calculate the probability of the event that infinitely many heads occur.

Suppose you repeatedly and independently roll a pair of fair dice and each time record the sum of the dice. What is the probability that an outcome of 5 appears before an outcome of 7 ? Justify your answer.

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