Probability 07

Random variables

Exercise

Let there be two players playing chess with each other. The moment one of them wins the game, the competition stops with a winner. If there is no winner in the first 10 games, the competition also stops, with a draw. The probability that the first player wins is , the probability that the second wins is and for the draw it is

Exercise

Exercise

A deck of cards numbered 1 through is shuffled and is to be turned over one card at a time. Before each cards is shown you are to guess which card it will be. The strategy that maximizes the expected number of guessed cards turns out to be guessing 1 continuously until correct, then go on to guessing 2, and so on.

Exercise

Exercise

A salesman has two appointments to sell vacuum cleaners. His first appointment will lead to a sale with probability and the second with probability Any sale is equally likely to be for 500$$