Section 5.2 The Addition Rule and Complements. Definition Two events are disjoint if they have no outcomes in common. Another name for disjoint events.

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Presentation transcript:

Section 5.2 The Addition Rule and Complements

Definition Two events are disjoint if they have no outcomes in common. Another name for disjoint events is mutually exclusive events.

Addition Rule – P( A or B) (Disjoint Events) Event A occurs or event B occurs P(E or F) = P(E) + P(F)

General Addition Rule P( A or B) Event A occurs or event B occurs or they both occur P(E or F) = P(E) + P(F) – P(E and F)

Complement of E To calculate, find the probability of E occurring and subtract from one. Consists of all outcomes m which event E does not occur. P(E C ) = 1 – P(E)

1. List the Outcomes Given S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, E = {1, 2, 3, 4, 5}, F = {1, 3, 5, 7, 9}, G = {8, 10} a)E C b)E or F c)E or G

2. Find the following probabilities P(E) = 0.20 and P(F) = 0.30 a)P(E or F) if P(E and F) = 0.10 b)P(E and F) if P(E or F) = 0.25 c)P(E or F) if E and F are mutually exclusive d)P(E C ) e)P(F C )

3. Find the following probabilities P(E) = 0.30, P(E or F) = 0.90 and P(E and F) = 0.05), Find P(F)

4. Find the probability ColorProbability Red0.20 Blue0.30 Green0.10 Yellow0.40 a)Find the probability of getting red b)Find the probability of getting red or blue c)Find the probability of not getting yellow

5. Find the probability AgeNumber of Hours a)Find P(20-29) b)Find P(40 or greater)

6. Find the probability Given a standard deck of cards and a card is pulled out at random: a)P(Diamond or King) b)P(Ace or Queen) c)P(Clubs or Heart) d)P(Red Card or Queen)

7. Find the probability Total Uses Facebook Uses Google Total a)If someone is chose at random, what is the probability they use Facebook? b)If someone is chose at random, what is the probability they are 24-26? c)If someone is chose at random, what is the probability they are a Google+ user? d)If someone is chose at random, what is the probability they are or a Facebook user?