homework4_solutions

# homework4_solutions - Math 1011 Intro to Statistics Spring...

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Math 1011– Intro to Statistics Spring 2011 HOMEWORK 4 Due Friday, 2/25/11 1. A 12-sided die has 3 sides painted red, 4 sides painted blue, 4 sides painted green, and 1 side painted black. (a) If the die is rolled 4 times, find the probability of at least 1 red (b) If the die is rolled 4 times, find the probability of 3 or fewer greens (c) Find the probability of exactly one red in four rolls. (d) Find the probability of exactly two blues in four rolls. Solution: (a) 1 - ( 9 12 ) 4 = 1 - ( 3 4 ) 4 = 256 - 81 256 = 175 256 (b) 1 - ( 4 12 ) 4 = 1 - ( 1 3 ) 4 = 81 - 1 81 = 80 81 (c) ( 4 1 ) ( 3 12 )( 9 12 ) 3 = 4( 1 4 )( 3 4 ) 3 = 27 64 (d) ( 4 2 ) ( 4 12 ) 2 ( 8 12 ) 2 = 6( 1 3 ) 2 ( 2 3 ) 2 = 24 81 = 8 27 2. Two cards are drawn from a 52 card deck. (a) Find the probability of exactly 0 spades. (b) Find the probability of exactly 1 spades. (c) Find the probability of exactly 2 spades. Solution: (a) ( 13 0 )( 39 2 ) ( 52 2 ) = 39 · 38 52 · 51 = 19 34 (b) ( 13 1 )( 39 1 ) ( 52 2 ) = 13 · 39 · 2 52 · 51 = 13 34 (c) ( 13 2 )( 39 0 ) ( 52 2 ) = 13 · 12 52 · 51 = 1 17 3. Four cards are drawn from a 52 card deck. (a) Find the probability of exactly 0 diamonds. (b) Find the probability of exactly 1 diamonds.

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