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HW3 solutions

# HW3 solutions - 2308 455 105 Pr 105 1 7 1 3 1 5 = = = = A A...

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STAT 2004 Homework 3 – Solutions Fall 2007 1. Let A = event we get three red balloons ) ( ) ( ] Pr[ S n A n A = n(A) = # ways to get three red balloons n(S) = # ways to get three balloons, regardless of color 0769 . 455 35 ] Pr[ 455 )! 3 15 ( ! 3 ! 15 3 15 ) ( 35 1 * 35 )! 0 8 ( ! 0 ! 8 * )! 4 7 ( ! 3 ! 7 0 8 3 7 ) ( = = = - = = = = - - = = A S n A n

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2. Let A = event we get exactly 1 blue balloon (and two of any other color) n(A) = # ways to get 1 blue and 2 red or yellow 4945 . 455 225 ] Pr[ 225 45 * 5 )! 2 10 ( ! 2 ! 10 * )! 1 5 ( ! 1 ! 5 2 10 1 5 ) ( = = = = - - = = A A n
3. Let A = event we get at least 1 yellow balloon (and the rest are any other color) Pr[A] = Pr[1 yellow] + Pr[2 y] + Pr[3 y] 5165 . 455 235 455 1 36 198 ] Pr[ 455 1 455 0 12 3 3 ] 3 Pr[ 455 36 455 12 * 3 455 1 12 2 3 ] 2 Pr[ 455 198 455 66 * 3 455 2 12 1 3 y] Pr[1 = = + + = = = = = = = = = A y y

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4. Let A = event we get one of each color
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Unformatted text preview: 2308 . 455 105 ] Pr[ 105 1 7 1 3 1 5 ) ( = = = = A A n 5. Using the chart from the lecture notes on probability, we get: 3 2 36 24 ] Pr[ 36 ) ( 24 ) ( = = = = A S n A n 6. Using the chart from the lecture notes, we get: 1111 . 36 4 ] Pr[ 4 ) ( = = = A A n 7. Let A = event we pick 5 juniors 56 5 8 ) ( = = A n 8. Let A = event we pick one from each class 10080 1 3 1 6 1 8 1 7 1 10 ) ( = = A n 9. 5! = 5*4*3*2*1=120 10. 5 5 = 3125...
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HW3 solutions - 2308 455 105 Pr 105 1 7 1 3 1 5 = = = = A A...

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