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Practice_Problems_Midterm1

B denote p pra scores 79120 q prb scores

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Unformatted text preview: = (20 choose 5) x (15 choose 5) Since all possibilities are equally likely, Answer = Pr(A) = (20 choose 5) x (15 choose 5) / ( (20 choose 5) x (20 choose 5) ) b) Let B = event that the first problem picked by Sundar is different from the first problem picked by Viveck. We need Pr(A|B) Pr(B) = 19x20/(20 x 20) = 19/20. Pr( A,B) = Pr (A and B) = Pr(A) Answer = Pr(A) / (19/20) Problem 3. a) Let Pr(A scores) = Pr(2 red, 1 green or blue) + Pr(A picks 2 green, 1 red or blue) + Pr(A picks 2 blue, 1 green or red) = ( (5 choose 2) x 5 + 1 x 8 + (3 choose 2) x 7 ) / (10 choose 3) = 79/120 Pr(B scores) = Pr(Exactly 2 red balls) + Pr( 3 red balls) = ( (5 choose 2) x 5 + (5 choose 3) ) / (10 choose 3) = 1/2. b) Denote p = Pr(A scores) = 79/12...
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