3.4 Independent and Dependent Events

If you have two exams next Tuesday, what is the probability that you will pass both of them? How can you predict the risk that a critical computer network server and its backup will both fail? If you flip an ordinary coin repeatedly and get heads 99 times in a row, is the next toss almost certain to come up tails? You are dealing with compound events involving two or more separate events

Independent Events The occurrence of one event has no effect on the occurrence of another The two events don’t happen at the same time Example: A coin is flipped and turns up heads. What is the probability that the second flip will turn up heads? The first coin’s outcome has nothing to do with the second Probability of tossing heads a second time is 0.5

Example A coin is flipped four times and turns up heads each time. What is the probability that the fifth trial will be heads? 0.5 ! You might think “tails has to come up sometime” The coin has no memory of the past 4 trials Still 50/50 chance on each independent toss

Independent or Dependent? First EventSecond Event Attending a rock concert on Tuesday night Passing a final exam the following morning Eating chocolateWinning at checkers Having blue eyesHaving poor hearing Attending an employee training session Improving personal productivity Graduating from university Running a marathon dependent independent dependent independent

Independent or Dependent? First EventSecond Event Going to a mallBuying a new shirt Hitting a home run while at bat Catching a pop fly while in the field Staying up lateSleeping in the next day Completing your calculus review Passing your calculus exam Randomly selecting a shirt Randomly selecting a tie dependent independent dependent

Note What is the probability of randomly selecting two kings from a regular deck of cards? It depends on whether you replace the first king or not With replacement: independent events Without replacement: dependent events

Product Rule for Independent Events P(A  B) = P(A)P(B) Example: What is the probability of getting two tails in a row? A = getting one tails B = getting another tails P(A  B) = P(A)P(B)

Let’s check this! A = getting two tails in a row = {TT} S = {HH, HT, TH, TT} Therefore, the probability of getting two tails in a row is

Let’s learn about conditional probability!! Go to Jarvis/Pick Up/Data Management/Unit 3/3.5 Conditional Probability.notebook