TEST 1a FALL 09 - 1 NAME ISyE 3770 Test 1 a Solutions Fall...

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Unformatted text preview: 1 NAME ISyE 3770 Test 1 a Solutions Fall 2009 This test is 55 minutes long. You are allowed one cheat sheet. Put your nice, simple answers here... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 2 1. What is any subset of an experiments sample space called? Solution: Event. 2. Suppose that P (it rains today) = . 4, P (it rains tomorrow) = . 8, and P (it rains either day) = 0 . 9. Whats the probability that it rains both days? Solution: P (Today and Tomorrow) = P (Today) + P (Tomorrow)- P (Today or Tomorrow) = 0 . 4 + 0 . 8- . 9 = 0 . 3 . 3. If P ( A ) = 0 . 3, P ( B ) = 0 . 5, and P ( C ) = 0 . 5, and A , B , and C are independent, find the probability that none of A , B , and C occur. Solution: P ( A B C ) = P ( A ) P ( B ) P ( C ) = (0 . 7)(0 . 5)(0 . 5) = 0 . 175 . 4. TRUE or FALSE? P ( A ) = 1 implies that A is the entire sample space. Solution: FALSE. For example, S = [0 , 1], A = [0 , 1]- { . 5 } . 5. TRUE or FALSE? If (i) P ( A B ) = P ( A ) P ( B ), (ii) P ( A C ) = P ( A ) P ( C ), and (iii) P ( B C ) = P ( B ) P ( C ), then A , B , and C are all independent of each other. Solution: FALSE. We also need P ( A B C ) = P ( A ) P ( B ) P ( C ). 6. Which is bigger, P 100 , 50 or 100 50 ?...
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This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Institute of Technology.

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TEST 1a FALL 09 - 1 NAME ISyE 3770 Test 1 a Solutions Fall...

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