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Unformatted text preview: EE 131A Midterm Solution Probability Fall 2005 Instructor: Vwani Roychowdhury 1. (a) P [ A ∩ B ] = P [ A  B ] P [ B ] = 0 . 1 P [ A ∪ B ] = 0 . 8 = P [ A ] + 0 . 2 . 1 → P [ A ] = 0 . 7 (b) Since P [ A  B ] negationslash = P [ A ], they are NOT independent. P [ A ∩ B ] negationslash = 0, hence they are NOT mutually exclusive. (c) P [( A ∪ B ) c ] = 1 P [ A ∪ B ] = 0 . 2 P [ B c  A c ] = P [ B c ∩ A c ] P [ A c ] = P [( A ∪ B ) c ] 1 P [ A ] = 2 / 3 2. (a) 1 parenleftBig 6 4 parenrightBig (b) There are only two ways to get at least 20 points, and those are 3 or 4 correct answers. Pr [ at least 20 points ] = Pr [EXACTLY 3 correct answers ] + Pr [EXACTLY 4 correct answers ] = ( 1 4 ) 3 3 4 parenleftBigg 4 3 parenrightBigg + ( 1 4 ) 4 parenleftBigg 4 4 parenrightBigg 3. (a) Let B and A designate the events that (i) the first three princes are NOT hemophil iacs, and (ii) the queen is a carrier, respectively. From the statements of the 1 problem it follows that, P [ A ] = 1...
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This note was uploaded on 03/27/2012 for the course EE EE 131A taught by Professor Roychowdhary during the Spring '05 term at UCLA.
 Spring '05
 Roychowdhary

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