Compound Probability Pre-AP Geometry

Compound Events are made up of two or more simple events. I. Compound Events may be: A) Independent events - when the outcome of one does not affect the outcome of another P (A and B) = P (A)  P (B) Example: A bin contains 4 green marbles, 2 black marbles, 5 red marbles, and 6 yellow marbles. P (drawing a green marble, replacing it, then drawing a red) = 4 / 17  5 / 17 = 20 / 289 **Since the first marble drawn is being replace before the next one is drawn, one probability is independent from the next.

B) Dependent events – when the outcome of one event effects the outcome of another P (A and B) = P (A)  P (B following A) Example: A bin contains 4 green marbles, 2 black marbles, 5 red marbles, and 6 yellow marbles. P (drawing a green marble, then drawing a red, without replacement) = 4 / 17  5 / 16 = 20 / 272 = 5 / 68 **Since the first marble drawn is not being replace before the next one is drawn, one probability dependents on the next.

C) Mutually Exclusive events - when the events cannot occur at the same time P (A or B) = P (A) + P (B) Example 1: A bin contains 4 green marbles, 2 black marbles, 5 red marbles, and 6 yellow marbles. P (yellow or black, with replacement) = 6 / / 17 = 8 / 17 Example 2: A bin contains 4 green marbles, 2 black marbles, 5 red marbles, and 6 yellow marbles. P (yellow or black, without replacement) = 6 / / 16 = 130 / 272 = 65 / 136 ** Since the probabilities are mutually exclusive, then the probability the either can occur is just the sum of the probabilities. ** when not specified, assume it is with replacement

II. A bag contains 2 red, 5 blue, and 8 yellow marbles. Find each probability. A) P (yellow, replacing it, then red) B) P (blue, replacing it, then red) C) P (blue and red, without replacement) D) P (yellow and blue, without replacement) E) P (yellow or blue) F) P (yellow or red, without replacement)

III. A card is drawn from a standard deck of 52 cards. Find each probability. Standard deck: 13 hearts, 13 diamonds, 13 spades, and 13 clubs 26 red and 26 black 4 of each # 2-10, Jack, Queen, King, and Ace Face cards are Jack, Queen and King A) P (face card, replacing it, then an Ace) B) P (Jack then a 4, without replacement) C) P (King or 3) D) P (King or 3, without replacement)