Finding expected value and median. Continue reading
From the integers 1, 2, … 52, I choose seven (distinct) integers at random, all choices being equally likely. From these seven, I discard any pair that sum to 53. Let X be the random variable the value of which is the number of discarded pairs. Find the probability distribution of X and show that E(X) = 7 / 17 Continue reading
Three married couples sit down at a round table at which there are six chairs. All of the possible seating arrangements of the six people are equally likely.
(i) Show that the probability that each husband sits next to his wife is 2/15
(ii) Find the probability that exactly two husbands sit next to their wives.
(iii) Find the probability that no husband sits next to his wife. Continue reading