DISCRETE MATHEMATICS

DISCRETE MATHEMATICSPROBABILITYCS 137: DISCRETE MATHEMATICSPROBABILITYused in games analysis as early as 15th century.Nowadays, it is an indispensable tool in decision making and risk management.

Examples:There is a 90% chance of rain tomorrow according to a weather station.The doctor says there is a 50% chance of survival for him after this operation.CS 137: DISCRETE MATHEMATICSTERMS:EXPERIMENT process/ activity that yields an outcome.

EVENT an outcome or combination of from an experiment.

SAMPLE SPACE consists of all possible outcomes.

CS 137: DISCRETE MATHEMATICSILLUSTRATION:Consider rolling two dice and the numbers that will show up are the same.

Consider taking two cards from a regular deck of 52 cards and getting two aces.

CS 137: DISCRETE MATHEMATICSDEFINITION: CS 137: DISCRETE MATHEMATICSFind the probability that when a dice is rolled, it will be a prime number.Find the probability that when two card is drawn from a shuffled deck of 52 cards, both will be aces.Find the probability that when two fair dice are rolled, the sum will be 11.Five microprocessors are selected from a lot of 1000 microprocessors, among which 20 are defective. Find the probability of obtaining (a) no defective microprocessors. (b) exactly two defective microprocessors (c) at least one defective microprocessor.

CS 137: DISCRETE MATHEMATICSDEFINITION: CS 137: DISCRETE MATHEMATICSSOME PROBABILITY RULES: CS 137: DISCRETE MATHEMATICSSOME PROBABILITY RULES: CS 137: DISCRETE MATHEMATICSSOME PROBABILITY RULES: CS 137: DISCRETE MATHEMATICSIn a family of four children, what is the probability of having exactly two girls? Of at least one boy?Suppose a coin is flipped 10 times, what is the probability of no heads turning up/ of exactly five heads turning up? Of at least one head turning up?Suppose a professional wrestler is selected at random among 90 wrestlers, where 35 are over 350 pounds, 20 are bad guys and 15 are over 350 pounds and bad guys. What is the probability that a wrestler selected is over 350 pounds or a bad guy?CS 137: DISCRETE MATHEMATICSDEFINITION: CS 137: DISCRETE MATHEMATICSCompute the probability of getting a sum of 10, given that at least one die shows 5, when two fair die are rolled.

Weather records show that the probability of high barometric pressure is 0.80 and the probability of rain and high barometric pressure is 0.10. What is the probability of rain given high barometric pressure?CS 137: DISCRETE MATHEMATICSDEFINITION: CS 137: DISCRETE MATHEMATICSBAYES THEOREM: CS 137: DISCRETE MATHEMATICSA company buys computers from three vendors and tracks the number of defective machines as follows:

Find P(A), P(D), P(N), P(B|A), P(D|B) and P(B)

CS 137: DISCRETE MATHEMATICSAzeus (A)DotCom (D)Nuclear (N)% purchased551035% defective (B)1332. The enzyme-linked immunosorbent assay (ELISA) test is used to detect antibodies in blood and can indicate the presence of HIV virus. Approximately 1.5% of the patients in a certain clinic have HIV virus. Furthermore, among those that have HIV virus, approximately 95% test positive on ELISA test. Among those that do not have HIV virus, about 2% test positive on ELISA test. Find the probability that a patient has HIV virus given that his ELISA test is positive.CS 137: DISCRETE MATHEMATICS