 # WARM UP Students that were here last class, get with your groups and finish your Mutually Exclusive problems New students wait until attendance is called.

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WARM UP Students that were here last class, get with your groups and finish your Mutually Exclusive problems New students wait until attendance is called and Ms. Russell or Ms. Ross will get you settled and caught up with the lesson. Welcome!

COMPOUND EVENTS: MUTUALLY EXCLUSIVE AND DEPENDENT EVENTS Georgia Standard MM1D2. Students will use the basic laws of probability.

GEORGIA PROFESSIONAL STANDARD MM1D2. Students will use the basic laws of probability mutually exclusive a. Find the probabilities of mutually exclusive events. dependent b. Find the probabilities of dependent events.

ESSENTIAL QUESTION How does the occurrence of one event affect the occurrence or probability of another event?

OBJECTIVE 1) Students should be able to recognize the differences between mutually exclusive events and overlapping events. 2) Students should be able to recognize the differences between independent and dependent events. 3) Students should be able to name real life examples

REVIEW DEFINITIONS Mutually Exclusive Events – two events that have no common outcome They are mutually exclusive if they cannot occur at the same time Overlapping Events – have at least ONE common outcome Day Heads Even SEC Night Tails Odd ACC

FORMULAS Mutually Exclusive FormulaOverlapping Formula If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B) If A and B are overlapping events, then P(A or B) = P(A) + P(B) – P(A and B) This is the common event A and B share A B BA

EXAMPLE Mutually Exclusive Overlapping Event A: Choosing a Queen Event B: Choosing a 3 Event A: Choosing a Queen Event B: Choosing a club Overlap = Queen of Clubs Event A: Rolling a 5 on a die Event B: Rolling an odd number Overlap = 5 OR Rule = ADD AND Rule = MULTIPLY OR Rule = ADD AND Rule = MULTIPLY

Are these events Mutually Exclusive or Overlapping? Throw a dice and get a 2 and even number. Throw a dice and get a 2 and even number. Pick a card and get a red card and an spade. Pick a card and get a red card and an spade. Pick a heart and an ace. Pick a heart and an ace. Throw a dice and get a 4 and a prime number Throw a dice and get a 4 and a prime number Mutually Exclusive and Overlapping Examples

Throw a dice and get a 2 and an even number. Throw a dice and get a 2 and an even number. Overlapping Pick a card and get a red card and an spade. Pick a card and get a red card and an spade. Mutually Exclusive Pick a heart and an ace. Pick a heart and an ace. Throw a dice and get a 4 and a prime number Throw a dice and get a 4 and a prime number Overlapping Mutually Exclusive

LETS SEE SOME MORE PROBLEMS EACH GROUP PRESENT THEIR MUTUALLY EXCLUSIVE INDIVIDUALS WILL PRESENT OVERLAPPING

MORE DEFINITIONS Mutually Exclusive Events – two events are mutually exclusive if they cannot occur at the same time Overlapping Events – have at least ONE common outcome Independent Events – If the occurrence of one event has NO effect on the occurrence of the other. Dependent Events – If the occurrence of one event affects the occurrence of the other Cards Football Dice Basketball Golf

FORMULAS Independent Dependent If A and B are independent events, then the probability that both A & B occur is: P(A and B) = P(A) * P(B) If A and B are dependent events, then the probability that both A & B occur is: P(A and B) = P(A) * P(B/A) Given OR Rule = ADD AND Rule = MULTIPLY

COMPARING DEPENDENT AND INDEPENDENT EVENTS You randomly select two cards from a standard 52-card deck. What is the probability that the first card is not a face card (a king, queen, or jack) and the second card is a face card if (a) you replace the first card before selecting the second, and (b) you do not replace the first card?

(A) If you replace the first card before selecting the second card, then A and B are independent events. So, the probability is: P(A and B) = P(A) P(B) = 40 * 12 = 480 = 30 52 52 2704 169 0.1775 (B) If you do not replace the first card before selecting the second card, then A and B are dependent events. So, the probability is: P(A and B) = P(A) P(B|A) = 40 *12 = 40 52 51 221.1810

RECALL: ESSENTIAL QUESTION How does the occurrence of one event affect the occurrence or probability of another event? P(A and B) or P(A or B)

THINGS TO REMEMBER P(A or B) P(A & B) Mutually Exclusive P(A) + P(B) Overlapping P(A) + P(B) – P(A and B) Independent Events P(A) * P(B) Dependent Events P(A) * P(B/A) Lets Practice!

NEXT CLASS Conditional Probability Analyze new datasets We will continue to practice relating probability to real life situations

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