1 Davis Chp. 2 – Elementary Statistics Probability (pp. 1124) Binomial Combinations Number of combinations of n items taken r at a time: ! ! = !! ! − ! ! !! Binomial Distribution – The classic coin toss example: r successes will occur in n trials ! = ! ! (1 − !) !!! ! ! = !! ! − ! ! !! (1 − !) !!! ! ! Negative Binomial – “How many wells do we have to drill before a r discoveries are made?” ! = (! + ! + 1)! ! − 1 ! !! (1 − !) ! ! ! Sampling with/without Replacement Hypergeometric Probability Distribution – “What are the chances of x discoveries out of n drill holes if N prospects contain S reservoirs?” ! = ! ! !!! !!! ! ! = !! ! − ! ! !! (! − !)! (! − !) − (! − !) ! (! − !)! !! ! − ! ! !! Mutually Exclusive Events and Additive Rule of Probability When only a discrete number of outcomes are possible and they are all mutually exclusive, then ! ! !" ! !" ! = ! ! + ! ! + !(!) Independent Events and the Multiplicative Rule of Probability Conditional Probabilities If harmonic tremors occur from magma movement in a volcano AND eruptions follow magma movement in a volcano, then there’s a relationship between harmonic tremors and eruptions, so the probability of a tremor AND an eruption occurring is not equal to the probability of a tremor X the probability of an eruption. Bayes’ Theorem – The joint probability that both events A and B occur is equal to the probability that B will occur given that A has already occurred times the probability that A will occur. Bayes’ Basic Equation: