12.4 Probability of Disjoint & Overlapping Events

Probability of Disjoint & Overlapping Events In your own words, write the meaning of each vocabulary term. compound event union or intersection of two events overlapping events events that are in the shared union disjoint or mutually exclusive events when events are not shared or Core Concepts Probability of Compound Events If A and B are any two events, then the probability of A or B is P(A or B) = P(A) + P(B) - P(A and 1 B)   ie Dice (1, 2, 3, 4, 5, 6) A = even B = greater than 4 P(A or B) = 3/6 + 2/6 - 1/6 = 4/6 = 2/3 If A and B are disjoint events, then the probability of A or B is P(A or B) = P(A) + P(B) ie Dice (1, 2, 3, 4, 5, 6) A = even B = 5 P(A or B) = 3/6 + 1/6 = 4/6 = 2/3 Extra Practice Events A and B are disjoint. P(A) = 2/3 and P(B) = 1/6. Find P(A or B). P(A or B) = P(A) + P(B) = 2/3 + 1/6 = 4/6 + 1/6 = 5/6 = 0.833 P(A) = 0.8, P(B) = 0.05, and P(A or B) = 0.6. Find P(A and B). P(A or B) = P(A) + P(B) - P(A and B) 0.6 = 0.8 + 0.05 - P(A and B) 0.6 = 0.85 - P(A and B) -0.25 = -P(A and B) 0.25 = P(A and B) In Exercises 3-6, a vehicle is randomly chosen from a parking lot. The parking lot contains three red minivans, two blue minivans, three blue convertibles, one black pickup truck, three black motorcycles, one red motorcycle, and two blue scooters. Find the probability of selecting the type of vehicle. 1   Type Minivans Convertibles Scooters Motorcycles Grand Total Red 3 1 4 Blue 2 3 2 7 Black 1 3 4 Total 6 3 2 4 15 A red vehicle or a minivan P(Red or Minivan) = P(Red) + P(Minivan) - P(Red and Minivan) = 4/15 + 6/15 - 3/15 = 9/15 - 3/15 = 6/15 = 0.4 A scooter or a black vehicle P(Scooter or Black) = P(Scooter) + P(Black) - P(Scooter and Black) = 2/15 + 4/15 - 0 = 6/15 = 0.4 A black vehicle or a motorcycle P(Black or Moto) = P(Black) + P(Moto) - P(Black and Moto) = 4/15 + 4/15 - 3/15 = 8/15 - 3/15 = 5/15 = 0.33 A four-wheeled vehicle or a blue vehicle P(4-wheeled or Blue) = P(4-wheeled) + P(Blue) - P(4-wheeled and Blue) = 9/15 + 7/15 - 5/15 = 16/15 - 5/15 = 11/15 = 0.73 12.4 During a basketball game, the coach needs to select a player to make the free throw after a technical foul on the other team. There is a 68% chance that the coach will select you and a 26% chance that the coach will select your friend. What is the probability that you or your friend is selected to make the free throw?   P(You or Friend) = P(You) + P(Friend) - 0 = .68 + .26 = .94 Two six-sided dice are rolled. Find the probability of rolling the same number twice. table showing the possible outcomes of rolling two dice 6/36 = 1/6 = 0.16 Out of 120 student parents, 90 of them can chaperone the Homecoming dance or the Prom. There are 40 parents who can chaperone the Homecoming dance and 65 parents who can chaperone the Prom. What is the probability that a randomly selected parent can chaperone both the Homecoming dance and the Prom?   twoway table showing the number of parents who can chaperone the Homecoming dance and/or the Prom P(H or P) = P(H) + P(P) - P(H and P) 90 = 40 + 65 - P(H and P) 90 = 105 - P(H and P) -15 = -P(H and P) 15/120 = 1/8 = 0.125 A football team scores a touchdown first 75% of the time when they start with the ball. The team does not score first 51% of the time when their opponent starts with the ball. The team who gets the ball first is determined by a coin toss. What is the probability that the team scores a touchdown first?   tree diagram showing the possible outcomes of a coin toss and the football team scoring first .5 * .75 = .375 .5 * .25 = .125 .375 + .125 = .5