11.7 Continued11.7 ContinuedProbabilityProbability

Independent EventsIndependent Events►Two events are independent if the Two events are independent if the

occurrence of one has no effect on the occurrence of one has no effect on the occurrence of the otheroccurrence of the other

►Probability of Independent EventsProbability of Independent EventsIf A and B are independent events, the If A and B are independent events, the probability that both A and B will occur isprobability that both A and B will occur isP(A and B) = P(A)*P(B)P(A and B) = P(A)*P(B)

Example 1Example 1►A random number generator on a A random number generator on a

computer selects three integers from 1 computer selects three integers from 1 to 20. What is the probability that all to 20. What is the probability that all three numbers are less than or equal three numbers are less than or equal to 5?to 5?

The Complement of an EventThe Complement of an Event►The complement of an event A is the The complement of an event A is the

collection of all outcomes in the sample collection of all outcomes in the sample space that are NOT in A.space that are NOT in A.

►Probability of a ComplementProbability of a ComplementLet A be an event and let A’ be its Let A be an event and let A’ be its complement. If the probability of A is complement. If the probability of A is P(A), the probability of the complement is P(A), the probability of the complement is P(A’) = 1 – P(A) P(A’) = 1 – P(A)

Example 2Example 2►A manufacturer has determined that a A manufacturer has determined that a

machine averages one faulty unit for machine averages one faulty unit for every 1000 it produces. What is the every 1000 it produces. What is the probability that an order of 200 units probability that an order of 200 units will have one or more faulty units?will have one or more faulty units?

HW HW ►Pg 873 # 49-53Pg 873 # 49-53