Assignment 2 Answers - MAT2378B: Assignment 1 Due date: 07...

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MAT2378B: Assignment 1 Due date: 07 October 2009 Total number of points: 34 Q 1. The three events are shown on the Venn diagram: ’$ A ’$ B ’$ C Reproduce the figure and shade the region corresponding to the following events: (a) A c (b) ( A and B ) or ( A and B c ) (c) ( A and B ) or C (d) ( B or C ) c (e) ( A and B ) c and C Solution to Q1: Marking scheme for Q1: Correct answer for each part - 1 point. Total - 5 points. Q 2. (Q3.5) In a certain college, 55% of the students are women. We take a sample of two students. Find the probability that (a) both are women; (b) at least on of the two students is a woman. Solution to Q2: (a) 0 . 55 × 0 . 55 = 0 . 3025 (b) 0 . 55 × 0 . 55 + 0 . 45 × 0 . 55 + 0 . 45 × 0 . 55 = 0 . 7975 Marking scheme for Q2: Correct answer for each part - 1 point. Total - 2 points. Q 3. If P ( A ) = 0 . 3, P ( B ) = 0 . 2, and P ( A and B ) = 0 . 1, determine the following probabilities: (a) P ( A c ) (b) P ( A or B ) (c) P ( A c and B ) (d) P ( A and B c ) (e) P (( A or B ) c ) (f) P ( A c or B ) Solution to Q3: (a) P ( A c ) = 1 - P ( A ) = 0 . 7 (b) P ( A or B ) = P ( A ) + P ( B ) - P ( A and B ) = 0 . 4 (c) P ( A c and B ) = P ( B ) - P ( A and B ) = 0 . 1 (draw a Venn diagram to see this) (d) P ( A and B c ) = P ( A ) - P ( A and B ) = 0 . 2
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(e) P (( A or B ) c ) = 1 - P ( A or B ) = 1 - 0 . 4 = 0 . 6 (f) P ( A c or B ) = P ( A c ) + P ( B ) - P ( A c and B ) = 0 . 7 + 0 . 2 - 0 . 1 = 0 . 8
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Assignment 2 Answers - MAT2378B: Assignment 1 Due date: 07...

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