text: TEST 1 FALL 10
  
  # TEST 1 FALL 10 - 1 NAME ISyE 3770 Test 1a Solutions Fall...
  
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  1 NAME ISyE 3770 — Test 1 a Solutions — Fall 2010 (revised 10/1/10) This test is 55 minutes long. You are allowed one cheat sheet. 1. TRUE or FALSE? If A 1 ,A 2 ,...,A n are disjoint events, then P ( n i =1 A i ) = n i =1 P ( A i ). Solution: TRUE. P ( A i A j ) = 0 for all i,j . 2. Suppose that P (It snows today | It’s cold outside) = 0 . 8 and P (It snows today and it’s cold outside) = 0 . 5 . Find the probability that it’s cold outside. Solution: P (Snow | Cold) = P (Snow and Cold) P (Cold) P (Cold) = P (Snow and Cold) P (Snow | Cold) = 5 8 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 all three of A , B , and C occur. Solution: P ( A B C ) = P ( A ) P ( B ) P ( C ) = 0 . 075. 4. Consider a box of 10 sox — 6 blue and 4 red. Pick two sox without replacement. What’s the probability that the second sock is red?
  
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  2 Solution: P (2nd is Red) = P (1st is Blue, 2nd is Red) + P (1st is Red, 2nd is Red) = ± 6 10 ¶± 4 9 + ± 4 10 ¶± 3 9 = 2 5 5. TRUE or FALSE? If A and B are independent, then A and B are disjoint. Solution: FALSE. For example, if A and B are independent, P ( A ) = 0 . 2 , P ( B ) = 0 . 5 and P ( A B ) = (0 . 2)(0 . 5) = 0 . 1 6 = 0. 6. What is 0! (zero factorial)? Solution:
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  TEST 1 FALL 10 - 1 NAME ISyE 3770 Test 1a Solutions Fall...
  
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explanation: The document is a test paper for a course in Industrial and Systems Engineering (ISyE 3770) from Fall 2010. It contains multiple math questions and their corresponding solutions. The questions are related to probability and statistics.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: TEST 1 FALL 10
  
  # TEST 1 FALL 10 - 1 NAME ISyE 3770 Test 1a Solutions Fall...
  
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  1 NAME ISyE 3770 — Test 1 a Solutions — Fall 2010 (revised 10/1/10) This test is 55 minutes long. You are allowed one cheat sheet. 1. TRUE or FALSE? If A 1 ,A 2 ,...,A n are disjoint events, then P ( n i =1 A i ) = n i =1 P ( A i ). Solution: TRUE. P ( A i A j ) = 0 for all i,j . 2. Suppose that P (It snows today | It’s cold outside) = 0 . 8 and P (It snows today and it’s cold outside) = 0 . 5 . Find the probability that it’s cold outside. Solution: P (Snow | Cold) = P (Snow and Cold) P (Cold) P (Cold) = P (Snow and Cold) P (Snow | Cold) = 5 8 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 all three of A , B , and C occur. Solution: P ( A B C ) = P ( A ) P ( B ) P ( C ) = 0 . 075. 4. Consider a box of 10 sox — 6 blue and 4 red. Pick two sox without replacement. What’s the probability that the second sock is red?
  
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  2 Solution: P (2nd is Red) = P (1st is Blue, 2nd is Red) + P (1st is Red, 2nd is Red) = ± 6 10 ¶± 4 9 + ± 4 10 ¶± 3 9 = 2 5 5. TRUE or FALSE? If A and B are independent, then A and B are disjoint. Solution: FALSE. For example, if A and B are independent, P ( A ) = 0 . 2 , P ( B ) = 0 . 5 and P ( A B ) = (0 . 2)(0 . 5) = 0 . 1 6 = 0. 6. What is 0! (zero factorial)? Solution:
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a test paper for a course in Industrial and Systems Engineering (ISyE 3770) from Fall 2010. It contains multiple math questions and their corresponding solutions. The questions are related to probability and statistics.
  
  Label: multiple-question-and-answer