Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being converted to probabilities, typically add to something greater than one. Why is this? Suppose you place a bet of $10 on this horse. It seems that it is a fair bet if you lose your $10 if the horse loses, but you win $90 if the horse wins. However, argue why this isn’t really fair to you, that is, argue why your expected winnings are negative.
Answer to relevant QuestionsThe results we obtain with conditional probabilities can be quite counterintuitive, even paradoxical. This case is similar to one described in an article by Blyth (1972), and is usually referred to as Simpson’s paradox. ...An investor has invested in nine different investments. The dollar returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $50,000 and standard ...The manufacturer of a particular bicycle model has the following costs associated with the management of this product’s inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle ...Continuing the previous exercise, use the normal approximation to the binomial to answer each of the questions posed in parts a through f. How well does the normal approximation perform in this case? Explain. a. What is the ...A firm’s office contains 150 PCs. The probability that a given PC will not work on a given day is 0.05. a. On a given day what is the probability that exactly one computer will not be working?b. On a given day what is the ...
Post your question