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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.

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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. 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Time!

  3. 2. Now, divide the right hand section into 4 sections by drawing 3 evenly spaced lines. 3. Use scissors to cut along your drawn line, but ONLY to the crease! The fold crease

  4. 4. Write COMPOUND EVENTS down the left hand side Compound Events

  5. 5. Fold over the top cut section and write MUTUALLY EXCLUSIVE EVENTS on the outside. On the remaining 3 flaps, write: OVERLAPPING EVENTS INDEPENDENT EVENTS and DEPENDENT EVENTS Compound Events Mutually Exclusive Events

  6. What is….. likelihood PROBABILITY odds chance possibility

  7. Probability is represented as the following ratio: P # of favorable outcomes P +R # of unfavorable outcomes } Total # of outcomes # of favorable outcomes

  8. Compound Event Combines two or more events, using the word AND or OR

  9. Mutually Exclusive Events Events that have no common outcomes Formula:

  10. Example 1 • What is the probability of a die showing a 2 or a 5?

  11. Mutually Exclusive Practice • The probabilities of three teams A, B and C winning a badminton competition are • Calculate the probability that • a) either A or B will win • b) either A or B or C will win • c) none of these teams will win • d) neither A nor B will win

  12. Solution/s c) P(none will win) = 1 – P(A or B or C will win) d) P(neither A nor B will win) = 1 – P(either A or B will win)

  13. Overlapping Events Events that have at least one common outcome Formula:

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

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

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

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

  18. 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.

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

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

  21. Example 1 • A purse contains four P50 bills, five P100 bills and three P20 bills. Two bills are selected without the first selection being replaced. Find P(P50, then P50)

  22. There are four P50 bills. • There are a total of twelve bills. • P(P50) = 4/12 • The result of the first draw affected the probability of the second draw. • There are three P50 bills left. • There are a total of eleven bills left. • P(P50 after P50) = 3/11

  23. Example 1 Cont… • P(P50, then P50) = P(P50) · P(P50 after P50) = (4/12)x(3/11)=12/132 • The probability of drawing a P50 bill and then a P50bill is

  24. 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)

  25. 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

  26. Example 1

  27. You Try!

  28. Example 2

  29. You Try!

  30. Example 3

  31. You Try!

  32. 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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