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6.4 Find Probabilities of Compound Events

6.4 Find Probabilities of Compound Events. p. 351. Vocabulary. Compound event: Combines 2+ events Using words and or the word or Mutually exclusive events: no common outcomes Overlapping events: 1+ common outcome. Vocabulary Continued.

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6.4 Find Probabilities of Compound Events

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  1. 6.4 Find Probabilities of Compound Events p. 351

  2. Vocabulary • Compound event: • Combines 2+ events • Using words and or the word or • Mutually exclusive events: no common outcomes • Overlapping events: 1+ common outcome

  3. Vocabulary Continued • Independent events: 1 event has no effect on the other • Color of your teacher’s hair and the grade on a test • Dependent events: 1 event affects the other event • Bad weather and number of automobile accidents • Conditional Probability: the probability that one event will occur because another one occurred

  4. Probability of mutually exclusive events If A and B are mutually exclusive, then P(A or B)= P(A) + P(B). Probability of overlapping events If A and B are overlapping, then P(A or B) = P(A) + P(B) – P(A and B) If A and B are independent, then P(A and B)= P(A) * P(B). Probability of Independent events Probability of Dependent events If A and B are dependent, then P(A and B)= P(A) * P(B given A).

  5. You roll a number cube. Find the probability that you roll a 2 or an odd number. SOLUTION

  6. Find the probability of A or B You roll a number cube. Find the probability that you roll an even number or a prime number.

  7. 1. You roll a number cube. Find the probability that you roll a 2 or a 5. 2. You roll a number cube. Find the probability that you roll a number less than 4 or an odd number.

  8. Find the probability of A and B PEN COLORS A box contains 3 blue pens and 5 black pens. You choose one pen at random, do not replace it, then choose a second pen at random. What is the probability that both pens are blue? SOLUTION Because you do not replace the first pen, the events are dependent. Before you choose a pen, there are 8 pens, and 3 of them are blue. After you choose a blue pen, there are 7 pens left and 2 of them are blue.

  9. 3. MARBLES A bag contains 4 red, 5 green, and 2 blue marbles. You randomly draw 2 marbles, one at a time. Find the probability that both are red if: a. You replace the first marble. b. You do not replace the first marble.

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