3.4 Independent and Dependent Events

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? dependent independent independent dependent independent

Independent or Dependent? dependent independent dependent dependent independent

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

3.4 Independent and Dependent Events