Independent Events

Independent Events That the occurrence of one event has no effect on the probability of occurrence of the second event. Angie Cook

Probabilities: Independent Events • Marginal probability – the probability of an event occurring: P(A) • Joint probability – the probability of multiple, independent events, occurring at the same time: P(AB) = P(A)*P(B) • Conditional probability – • The probability of event B given that event A has occurred: P(B/A) = P(B) • Or, the probability of event A given that event B has occurred: P(A/B) = P(A) Angie Cook

Problem 2-16 An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip drawn. What is the probability of …… Angie Cook

P(R) 8/20 = .40 P(G) 10/20 = .50 P(W) 2/20 = .10 1.00 Angie Cook

a) A white chip on the first draw? Marginal probability - P(A) P(W) = .10 Angie Cook

b) A white chip on the first draw and a red on the second? Joint probability for two independent events – P(AB) = P(A)*P(B) P(WR) = P(W) * P(R) .10 * .40 = .04 Angie Cook

c) two green chips being drawn? Joint probability for two independent events – P(AB) = P(A)*P(B) P(GG) = P(G) * P (G) .50 * .50 = .25 Angie Cook

d) A red chip on the second, given that a white chip was drawn on the first? Conditional probability – for independent events P(AB) = P(B) P(R/W) = P(R) P(R/W) = .40 Angie Cook

Independent Events