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Probability of Compound Events

Standards: MM1D2a. Find the probabilities of mutually exclusive events. b. Find the probabilities of dependent events. c. Calculate conditional probabilities. Probability of Compound Events. Independent Events. Events that have no effect on each other Formula:. Example 1.

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Probability of Compound Events

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  1. Standards: MM1D2a. Find the probabilities of mutually exclusive events.b. Find the probabilities of dependent events.c. Calculate conditional probabilities. Probability of Compound Events

  2. Independent Events Events that have no effect on each other Formula:

  3. Example 1 • If a dice is thrown twice, find the probability of getting two 5’s.

  4. Two sets of cards with a letter on each card as follows are placed into separate bags. Sara randomly picked one card from each bag. Find the probability that: a) She picked the letters ‘J’ and ‘R’. b) Both letters are ‘L’. c) Both letters are vowels.

  5. Solution for no. 2 • Probability that she picked J and R = • Probability that both letters are L = • Probability that both letters are vowels =

  6. Dependent Events Events where the occurrence of one affects the occurrence of another Formula:

  7. Example 1 • A purse contains four $50 bills, five $100 bills and three $20 bills. Two bills are selected without the first selection being replaced. Find P($50, then $50)

  8. There are four $50 bills. • There are a total of twelve bills. • P($50) = 4/12 • The result of the first draw affected the probability of the second draw. • There are three $50 bills left. • There are a total of eleven bills left. • P($50 after $50) = 3/11

  9. Example 1 Cont… • P($50, then $50) = P($50) · P($50 after $50) = (4/12)x(3/11)=12/132

  10. Dependent:Practice • A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. • a) Find P(red, then blue). • b) Find P(blue, then blue)

  11. Conditional Probability Used with DEPENDENT events: The probability that one event will occur given that another event has already occurred. EX. The probability of B given A; Key Concept: NON-REPLACEMENT

  12. Example 1

  13. You Try!

  14. Example 2

  15. You Try!

  16. Example 3

  17. You Try!

  18. Classify the compound events given below as either independent or dependent Rolling a die, then rolling a second die Drawing a card for a hand of poker, then drawing another card Picking a prize from a grab bag, then picking another Spinning a $100 slice on Wheel of Fortune, then spinning another $100 slice

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