TEST 1b FALL 09

# TEST 1b FALL 09 - 1 NAME → ISyE 3770 — Test 1 b...

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Unformatted text preview: 1 NAME → ISyE 3770 — Test 1 b 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 experiment’s sample space called? Solution: Event. ♦ 2. Suppose that P (it rains today) = . 7, P (it rains tomorrow) = . 8, and P (it rains either day) = 0 . 9. What’s the probability that it rains both days? Solution: P (Today and Tomorrow) = P (Today) + P (Tomorrow)- P (Today or Tomorrow) = 0 . 7 + 0 . 8- . 9 = 0 . 6 . ♦ 3. If P ( A ) = 0 . 3, P ( B ) = 0 . 3, 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 . 7)(0 . 5) = 0 . 245 . ♦ 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 , 40 or ‡ 100 60 · ?...
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TEST 1b FALL 09 - 1 NAME → ISyE 3770 — Test 1 b...

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