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Find Probabilities of Compound Events

Understand how to find probabilities for compound events by combining two or more events using 'and' or 'or'. Practice examples provided.

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Find Probabilities of Compound Events

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  1. Find Probabilities of Compound Events Lesson 6.4 Page 351

  2. AND OR This applies only for compound events!

  3. Compound Event A compound event combines two or more events, using the word and or the word or. • Example: • You choose a card from a standard deck of 52 playing cards. • Find the probability that you choose • A Queen OR an Ace • A King OR a Spade

  4. A Queen OR an Ace P(Queen) = P(Ace) = P(Queen or Ace) = P(Queen) + P(Ace) =

  5. LET’S COUNT 13 15 16 1 2 3 4 5 6 7 8 9 10 11 12 14 P(King) = P(Spade) = A King or a Spade WHAT HAPPENED?? P(King or Spade) = P(King) + P(Spade) =

  6. Mutually Exclusive vs.Overlapping Events Mutually Exclusive Events have no common outcomes. Overlapping Events have at least one common outcome.

  7. P(King) = P(Spade) = A King or a Spade P(King or Spade) = P(King) + P(Spade) - P(King and Spade)

  8. Now you try … • Find the probability that you choose • A heart or a spade • A card with an even number or a heart.

  9. Find the probability of compound events A quality inspector at a bolt manufacturer randomly selects 1 bolt from each batch of 50 bolts to inspect for defects. The first batch has 4 defective bolts . The second batch of 50 bolts has 5 defective bolts. Find the probability that the inspector selects a defective bolt BOTH times. Are these events independent or dependent? P(defect in batch 1) = P(defect in batch 2) = P(defect in batch 1 AND batch 2) =

  10. Now you try … A basket of apples contains 6 red apples, 2 green apples, and 3 yellow apples. Find the probability that both are yellow if you replace the first apple and then select the second apple. P(Yellow 1st Try) = P(Yellow 1st AND 2nd Try) = P(Yellow 2nd Try) =

  11. An aquarium contains 6 male goldfish and 4 female goldfish. You randomly select a fish from the tank, do not replace it, and then randomly select a second fish. What is the probability that both fish are male?

  12. Homework Assignment: Page 353 # 1 – 7 all

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