Paper 2, Section II, F

Probability | Part IA, 2015

When coin AA is tossed it comes up heads with probability 14\frac{1}{4}, whereas coin BB comes up heads with probability 34\frac{3}{4}. Suppose one of these coins is randomly chosen and is tossed twice. If both tosses come up heads, what is the probability that coin BB was tossed? Justify your answer.

In each draw of a lottery, an integer is picked independently at random from the first nn integers 1,2,,n1,2, \ldots, n, with replacement. What is the probability that in a sample of rr successive draws the numbers are drawn in a non-decreasing sequence? Justify your answer.

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