hw2_print

hw2_print - Total number of balls =30. 20 30 19 29 18 28 17...

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STAT416: Probability — Spring 2011 Assignments 1 Homework #2 (Solution) January 30, 2011 1 Total possible points is 35 1. Ex. 1.36 (5 pts) . xoo | xoo | xoo | xoo | xoo | xoo. There are 3 ways a male member can be in a committee, but since there are 6 committees the number of ways to have a male member in 6 committees is 3 6 . P (each committee contains 1 male member)= 3 6 18 6 = 6! · 12! · 3 6 18! . 2. Ex. 1.40 (5 pts) . There is n - r + 1 ways we can line up r people in n spots. n - r +1 n r = ( n - r +1) r !( n - r )! n ! 3. Ex. I.10 (5 pts) . Let A 1 = getting black ball in 10 draws, A 2 = getting white in 10 draws, A 3 = getting blue in 10 draws. P (at least one ball of each color) = P ( A 1 A 2 A 3 ) = 3 X i =1 P ( A i ) - 3 X i<j P ( A i A j )+ P ( A 1 A 2 A 3 ) = 3 ± 10 10 ² ± 30 10 ² - 3 ± 20 10 ² ± 30 10 ² + ± 30 10 ² ± 30 10 ² = 0 . 9816 . 4. Ex. I.11 (5 pts) . — — — — — B — — — —. 10 Black, 10 White, 10 Blue.
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Unformatted text preview: Total number of balls =30. 20 30 19 29 18 28 17 27 16 26 10 25 24 24 23 23 22 22 21 21 = 0 . 0435 . 5. Ex. I2.1 (5 pts) . True. P ( A B ) = P ( A ) + P ( B )-P ( A B ) = . 5 + . 25-P ( A B ) . 75 . 6. Ex. I2.4 (5 pts) . True. P (2nd is even)= P (1st is odd and 2nd is even) + P (1st is even and 2nd is even)= 50 100 50 99 + 50 100 49 99 = 1 2 . 7. Ex. I2.5 (5 pts) . True P (CHEESE) = 1 6 1 5 3 4 2 3 1 2 1 1 = 0 . 0083 &lt; . 5 . Purdue University hw2print.tex; Last Modied: January 30, 2011 (Prof. Sharabati)...
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