Compound Events – Independent and Dependent Chp. 8 Sec 2-B pg. 449-455

Compound Events Compound Events – two or more simple events Example: Rolling a number cube and flipping a coin. Independent Events – Events where the outcome of one does not affect the outcome of the other event. The above example is an independent event. Dependent Event – Events where the outcome of one event affects the outcome of another event. Example: A bag has 4 blue and 3 red marbles. You draw one marble out. WITHOUT REPLACING IT, you draw out a second marble. This is dependent because the first event “affects” the second event.

Compound Event We have a cup with 5 cubes in it, 4 red and 1 green. We draw one cube out, replace it and then draw a second cube. Is this an independent or dependent event? Independent – the first event does not affect the second event How about if you draw one cube out, DO NOT REPLACE and draw a second cube? Is it independent or dependent? Dependent

Compound Event Probability - Independent The probability of independent events is calculated by multiplying the probabilities together. P(A and B) = P(A) • P(B) We have a cup with 5 cubes in it, 4 red and 1 green. We draw one cube out, replace it and then draw a second cube. 1st cube is red. P(A) = 4 5 = 0.8 = 80% 2nd cube is green. P(B) = 1 5 = 0.2 = 20% P(A and B) = P(A) • P(B) P(A and B) = (0.8)(0.2) = 0.16 = 16%

Compound Event Probability - Dependent The probability of dependent events is calculated by multiplying the probability of A and then the probability of B after A occurs P(A then B) = P(A) • P(B following A) We have a cup with 5 cubes in it, 4 red and 1 green. We draw one cube out, do not replace it and then draw a second cube. 1st cube is red. P(A) = 4 5 = 0.8 = 80% 2nd cube is green. P(B) = 1 4 = 0.25 = 25% P(A then B) = (0.8)(0.25) = 0.2 = 20%