DEPENDENT AND INDEPENDENT EVENTS Objectives: How to find the probabilities of independent and Dependent Events How to find the probabilities of events given the occurrence of other events Compound Event – also known as composite event, consists of two or more simple events. Independent Event – the probability that occurs in an event, A, does not affect the probability that occurs in another event, B. Dependent Event - the probability that occurs in an event, B, changes the probability that occurs in another event, B. Identify Independent and Dependent Events a)One coin is tossed, and then a second coin is tossed b)In a class presentation, one student’s name is chosen and not replaced, and then a second name is chosen. c)Wednesday’s lottery numbers and Saturday’s lottery numbers

Supposed a coin is tossed, then the spinner is spun. What is the probability that the coin tossed is a head and the spinner’s needle lands in green

Marisol and her friends are going to a concert at Caldwell Auditorium in Tyler, Texas. They put the 5 yellow slips of paper and 3 blue slips of paper inside a bag. If a person draws a yellow slip, he or she will ride in the van to the concert. A blue slip means he or she rides in the car. Marisol, draw a slip. Not liking the outcome, She puts it back and draws a second time. What is the probability that Marisol will draw a blue slip

The notation P (B|A) is read the probability that event B occurs given that event A has already occurred. This is called conditional probability The same as previous example: Suppose Marisol draws a slip and does not put it back. Then her friend Christian draws a slip. What is the probability that both friends will draw a yellow slip P (Y and Y) = P(Y) x P(Y|Y)

PROBABILITY TREE, a graphic representation to show the possible outcome of two or more events In the drawing of slips, calculate the probability of each simple event at the first stage and each conditional probability at the second stage. Then multiply along each branch to find the probability of each outcome