# 01_26 - STAT 408 Examples for Spring 2009 3 Suppose S = cfw...

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STAT 408 Examples for 01/26/2009 Spring 2009 3. Suppose S = { 0, 1, 2, 3, … } and P( 0 ) = p , P( k ) = ! 2 1 k k , k = 1, 2, 3, … . Find the value of p that would make this a valid probability model. Must have = + 1 ! 2 1 k k k p = 1. Since a k k e k a 0 ! = = , 1 ! 2 1 2 1 1 - = = e k k k . Therefore, p + ( 1 2 1 - e ) = 1 and p = 2 1 2 e - . 4. The probability that a randomly selected student at Anytown College owns a bicycle is 0.55, the probability that a student owns a car is 0.30, and the probability that a student owns both is 0.10. P( B ) = 0.55, P( C ) = 0.30, P( B C ) = 0.10. C C ' B 0.10 0.45 0.55 B ' 0.20 0.25 0.45 a) What is the probability that a student selected at random does not own a bicycle? P( B ' ) = 1 – P( B ) = 1 – 0.55 = 0.45 . 0.30 0.70 1.00

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b) What is the probability that a student selected at random owns either a car or a bicycle, or both? P( B
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01_26 - STAT 408 Examples for Spring 2009 3 Suppose S = cfw...

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