Questions What is meant by the term risk? The danger or probability of loss, injury or death. What are the 4 major categories of risk? Give examples for each. See chart entitled Four Risk Categories. What is the difference between probability and statistics? Probability is a measure of the likelihood or chance that something will happen. Statistics are things that are measured or counted. What is meant by the term random? Random connotes absence of a pattern. What statistical distribution treats low probability events with small numbers of occurrences? Poisson distribution. What statistical distribution is used when we know the probability something will happen on each try, but want to know the probability that it will happen in a specified number of tries? Binomial distribution. What statistical distribution is used when we are measuring something rather than counting it? Normal distribution. What branch of statistics is used to predict results based on observed prior data? Frequentist statistics What branch of statistics is used to predict data based on observed prior results and makes use of subjective judgement? Bayesian statistics

Problems Assume each face of a die is equally likely to land facing up. Consider a game which involves the tossing of 5 dice. Find the probability that the number 1 appears uppermost a. On exactly one die b. In at least one die c. In exactly two dice

Problems, continued In Russian roulette (not recommended), one cartridge is loaded leaving the other 5 chambers of a revolver empty. The cylinder is then spun so that the loaded cartridge is at an unknown random position. What is the probability of still being alive after playing the game a. Once? b. Twice? c. N times?

A number is chosen at random between 0 and 1. What is the probability that exactly 5 of its first 10 decimal places consist of digits less than 5?

Problems, Contd A certain aircraft manufacturing plant averages 5 random defects per aircraft coming off the the assembly line. What is the probability that any given aircraft has zero defects? Ten defects?

A computer is built with 5 large scale integrated circuits (LSICs), each with a known mean time between random failures of 30,000 hours. Each is critical to the operation of the computer. (a) What is the probability that the computer will fail in the first 30 days of operation (warranty period)? (b) What is the probability the computer will fail in the first year? AND System Failure Probability P F4 P F3 P F2 P F1 P F5

A poll of 200 people concerning preference for one or the other of 2 candidates for the U.S. Senate shows one candidate in the lead by 10%. Should the poll be trusted to predict the election outcome?