quiz2 with soln

# quiz2 with soln - 4 P(A|B =0.1 P(A| B =0.2 P(B =0.7 P(A =...

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AMS310.01 QUIZ 2 September 17 PRINT YOUR NAME HERE__________________________________________ USE ALL UPPER CASE LETTERS. UNDERLINE YOUR LAST NAME STUDENT ID NUMBER__________________ _____ 1. P(A B)= 0.15 P(A)=0.5 P(B)= 0.2, P(B|A)= _____ 2. P(B|A) =0.8 P(A)=0.2 P(B)=0.6 P(A B)= ______ _____ 3. Given S= {1,2,3,4,5,6} the outcomes of the toss of 1 die. Let A={we get more than 4 dots} and let B={we get less than 3 dots}. Which statement below is correct? (a) A and B independent events. A and B are mutually exclusive events. (b) A and B are dependent events. A and B are mutually exclusive events. (c) A and B are independent. A and B are not mutually exclusive. (d) A and B are dependent events. A and B are not mutually exclusive.

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Unformatted text preview: ____ 4. P(A|B) =0.1 P(A| B ) =0.2 P(B) =0.7. P(A) =____ SOLUTIONS : 1. 15/50=0.30 3 . 50 . 15 . ) ( ) ( ) / ( = = ∩ = A P B A P A B P 2. 0.16 16 . ) 2 . ( * ) 8 . ( ) ( * ) / ( ) ( = = = ∩ A P A B P B A P 3. b A={ 5,6 }; so P(A)=2/6=1/3. B= { 1,2} , so P(B)=1/3. A ∩ B = { }, so P(A B )=0/6 and A and B are MUTUALLY EXCLUSIVE. Mutually exclusive events are always dependent. Or note that P(A)P(B) = (1/3) (1/3) = 1/9 ≠ 0 = P(A B); thus A, B are dependent .. 4. 0.13 P(A) = ) ( ) | ( 1 j n j j B P B A P ∑ = . Here n=2 and B 1 =B and B 2 = B so P(A) = P(A|B)P(B) + P(A| B ) P( B ) = (0.1 x 0.7) + (0.2 x 0.3) =0.13...
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