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University of California - Santa Cruz

Applied Math and Statistics

AMS 5

Yonatan Katznelson

Spring

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AMS 5 Lecture 12 532017 (8:009:05) *Note: There was no class Monday due to a protest Probability: Continued Example 5: What is the probability that a marble drawn at random from the (same) urn is red and makred with a B? o Recall Example2: 40 blue marbles A, o There are 100 marbles in the urn and 30 of them are both red and marked with a B, so P(red and B) = 30100 = 30 OR o 40 of the marbles in the urn are red, and of these red marbles, 75 are marked with a B, so P(red and B) = (40) * (75) = 30 o In other words P(red and B) = P(red) * P(B red) o The Multiplication rule. Given two events E and F P(E and F) = P(E) * P(F E) o Also P(E and F) = P(F) * P(E F) Example 6: Three cards are dealt from the top of a wellshuffled deck. What is the probability that the first card is a King and the third card is a 7? o The probability that the first card is a King is 452 and the probability that the third card is a 7 given that the first card is a King is 451, so o P(first card King and third card 7) = P(first card King) * P(third card 7 first card King) = 452 *451 = 162652 ~ .6 o Observation: The second card is unknown and so for all intents and purposes it is just another card in the deck. We dont talk about things we dont know (in this case the second card, so we discount it; even if he asked for the 51 card instead of the third card)

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