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Warm-up

This text explains the concepts of independent and dependent events in probability, using examples of rolling a number cube and selecting cards. It also covers mutually exclusive and overlapping events. Worksheets and practice questions are included for further understanding.

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Warm-up

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  1. State if the events are independent or dependant and find each probability. Warm-up Independent. P(2)=1/6 P(greater than 4)= 2/6 P(2,then greater than 4) = 1/18 Independent. P(T,T,T) = ½ x ½ x ½ = 1/8 You roll a number cube once. Then roll it again. What is the probability that you get 2 on the first roll and a number greater than 4 on the second roll? You toss a coin 3 times. What is the probability you get 3 tails? You have 7 cards. Each card has a letter on it spelling out the word ALGEBRA. Without replacing a card, what is the probability of selecting: a) A, then G b) E, then A, then R Dependant. P(A, then G) = 2/7 x 1/6 = 1/21 Dependant. P(E,then A, then R)= 1/7 x 2/6 x 1/5 =1/105

  2. 14.8a Compound Events • The probability of two events occurring is called a ________________. Independent and dependent events are compound events. Two other types of events are also compound events…________________, and ______________________. Compound Events Mutually Exclusive Overlapping Events Mutually exclusive means they can not happen at the same time! Overlapping means they can happen at the same time! (You have to take out the duplicates)

  3. Review….. • Two events are INDEPENDENT if the occurrence of one event does not affect the occurrence of the other! (Replacement might be a hint) • Two events are DEPENDENT if the occurrence of one event does affect the occurrence of the other. (Non-replacement)

  4. Disjoint or Mutually exclusive Events! Two event are mutually exclusive if they have no outcomes in common. …….. …. Key Concept: If A and B are mutually exclusive events, then the probability of A or B is: P(A or B)= P(A) +P(B) Look for the word “ or “ It means addition

  5. Mutually Exclusive Ex. 1 A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10 or a face card? Disjoint event Event A= 10 Event B= Face Card P(A or B) = P(A) + P(B) P(A or B) =

  6. Overlapping or Inclusive Event Ex. 2 A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a face card or a spade? Event A=Face Card Event B= Spade As you can see from the Venn Diagram, being a spade and a face card at the same time is possible. P(A or B) = P(A)+P(B)-P(A and B)

  7. Your turn to practice • Ex. 3 What is the probability of rolling a standard six-sided number cube and getting a 3 or a 5. • Ex. 4 You roll a number cube. What is the probability that you get an odd number or a number greater than 3? P(3) = 1/6 P(5)= 1/6 P(3 or 5)= 1/6 + 1/6 = 1/3 Solution: find the probability of the events. Let event A be getting an odd number and let Event B be getting number greater than 3. P(A)=3/6 P(B)= 3/6 P(A and B) = 1/6 P(A or B) = 3/6 + 3/6 – 1/6 = 5/6 0.83

  8. Summary Name two examples of compound events and if they would be independent, dependant, mutually exclusive, or overlapping?

  9. Homework time • Worksheet 14.8 ALL….make sure you have the right type of compound event: Is it Independent? Dependent? Mutually Exclusive? Overlapping? • IT makes a difference: the word and means: Multiply. The word or means add

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