Unformatted text preview: / 5. There is a weather forecast in the morning. If a rainy day is forecasted, it rains with probability 3 / 4 and if a dry day is forecasted, it is dry with probability 2 / 3. Mr. Pickwick listens to the forecast. If a rainy day is forecasted, he takes his umbrella before going out. If a dry day is forecasted, he takes his umbrella with probability 1 / 3. What is the probability that the day is dry, given that Mr. Pickwick took his umbrella? 4. Problem. There are three roads from city A to city B and there are two roads from city B to city C . Each of the ±ve roads is blocked with probability p , independently of the others. What is the probability that one can travel from city A to B given that there is no open route from A to C ? 5. Problem. We toss a fair coin till the coin lands 10 heads in total. What is the probability that we make 20 tosses altogether? 1...
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 Winter '12
 AlexanderBarvinok
 Forecasting, Probability, Mr. Pickwick

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