Dependent Events

Sometimes the outcome of an event can depend directly on the outcome of another event. Sometimes the outcome of an event can depend directly on the outcome of another event. When this happens, the events are said to be Dependent Events When this happens, the events are said to be Dependent Events

Conditional Probability The Conditional Probability of an Event B. Is the probability that B occurs GIVEN that A has already occurred

Ex A Professional hockey team has 8 Wingers. Three of these wingers are considered very good players or snipers. Every fall the team plays an exhibition match with the club’s farm team. In order to make the match more interesting for the fans, the coaches agree to select two wingers at random from the pro team to play for the farm team. What is the probability that the two pro wingers that will play for the farm team will be the snipers?

Let A represent the event that the first winger is a sniper Let B represent the event that the second winger is a sniper Three of the Eight are picked from the pro team. So the probability of a Pro winger being selected is If the first winger selected is one of the good players, then there are seven remaining wingers to choose from, two of which are the good players

The Probability that 2 snipers will be selected is Note: even though the events are dependent upon each other you can still multiply probabilities to find the probability that they both happen.

Product Rule for Dependent Events The Probability that dependent events will occur is given by

Ex Grace’s Computer sometimes crashes when she uses her Program. Her program stops responding to command she can usually close the program without the computer crashing. The Probability that her will not respond to commands is 2.5% and the chance that both and computer crash is 1%. If Grace’s is failing what is the probability that the computer will crash?

Let A be the event that Graces fails Let B be the event that the Computer Crashes Since event A triggers event B they are dependent upon each other. The probability of the computer crashing depends on if the fails

Summary Note If A and B are independent events then the probability of both events occurring is given by If event B is dependent upon event A, then the conditional probability of B given A is P(B | A). In this case the probability of both events

Homework! Pg 334 #5,6,8,10