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Lecture13[1]

# Lecture13[1] - independence – P(A∩B ∩C = P(A)P(B)P(C...

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Independence Section 4.4 1 STAT 225, Dallas Bateman, Spring 2010 Lecture 13

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Independence Two events are independent if the occurrence of one of the events gives us NO information about whether or not the other event will occur; that is, the events have no influence on each other. 2 STAT 225, Dallas Bateman, Spring 2010
Independence In probability theory we say that two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events: P(A∩B) = P(A)P(B) 3 STAT 225, Dallas Bateman, Spring 2010

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Independence The idea of independence can be extended to more than two events. For example, A, B and C are independent if: A and B are independent; A and C are independent and B and C are independent (pairwise

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Unformatted text preview: independence); – P(A∩B ∩C) = P(A)P(B)P(C) 4 STAT 225, Dallas Bateman, Spring 2010 Independence Example • Suppose that a man and a woman each have a pack of 52 playing cards. Each draws a card from his/her pack. Find the probability that they each draw the ace of clubs. 5 STAT 225, Dallas Bateman, Spring 2010 Independence Example • We define the events: – A = probability that man draws ace of clubs = 1/52 – B = probability that woman draws ace of clubs = 1/52 • Clearly events A and B are independent so: P(A∩B) = P(A)P(B) = 1/52 * 1/52 = 0.00037 That is, there is a very small chance that the man and the woman will both draw the ace of clubs. 6 STAT 225, Dallas Bateman, Spring 2010...
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