text: fall 2006 STAT 230 Quiz2Solutions
  
  # fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz#2 3:40...
  
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  Unformatted text preview: STAT 230 Quiz #2 Oct 12, 2006 3:40 – 4:10 pm Name: S I.D: UWUserid: Mark /20 Circle your instructor and time slot: 1. Metzler(1:30) 2. Drekic(11:30) 3. Springer(10:30) 4. Drekic(12:30) 5. Ramirez(8:30) 1. I have two coins. Coin A shows heads 50% of the time, Coin B shows heads 80% of the time. One of the coins is chosen at random, and that coin is flipped 5 times (each coin is equally likely to be chosen). [4] (a) What is the probability I get 5 consecutive heads? P (5H) = P (5H | A chosen) P (A chosen) + P (5H | B chosen) P (B chosen) = ( . 5) 5 ( . 5) + ( . 8) 5 ( . 5) = . 179465 [4] (b) Given that I got 5 consecutive heads, what is the probability that Coin B was chosen? P (B chosen | 5H) = P (5H | B chosen) P (B chosen) P (5H) = ( . 8) 5 ( . 5) . 179465 = . 9129 [3] (c) Are the events “Coin B chosen” and “5 consecutive heads” independent? Justify your answer. These events are not independent. There are several acceptable ways to show this P (5H ∩ B chosen) = ( . 5)( . 8)...
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  ## This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.
  
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  fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz#2 3:40...
  
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explanation: The provided text is a solution set for a STAT 230 quiz from Fall 2006. It contains solutions to a math question involving probability calculations with two different coins. The document includes parts (a), (b), and (c) of the question, each with a detailed solution. The question is about calculating the probability of getting 5 consecutive heads, determining the probability that a specific coin was chosen given 5 consecutive heads, and assessing the independence of the events "Coin B chosen" and "5 consecutive heads."
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: fall 2006 STAT 230 Quiz2Solutions
  
  # fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz#2 3:40...
  
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  Unformatted text preview: STAT 230 Quiz #2 Oct 12, 2006 3:40 – 4:10 pm Name: S I.D: UWUserid: Mark /20 Circle your instructor and time slot: 1. Metzler(1:30) 2. Drekic(11:30) 3. Springer(10:30) 4. Drekic(12:30) 5. Ramirez(8:30) 1. I have two coins. Coin A shows heads 50% of the time, Coin B shows heads 80% of the time. One of the coins is chosen at random, and that coin is flipped 5 times (each coin is equally likely to be chosen). [4] (a) What is the probability I get 5 consecutive heads? P (5H) = P (5H | A chosen) P (A chosen) + P (5H | B chosen) P (B chosen) = ( . 5) 5 ( . 5) + ( . 8) 5 ( . 5) = . 179465 [4] (b) Given that I got 5 consecutive heads, what is the probability that Coin B was chosen? P (B chosen | 5H) = P (5H | B chosen) P (B chosen) P (5H) = ( . 8) 5 ( . 5) . 179465 = . 9129 [3] (c) Are the events “Coin B chosen” and “5 consecutive heads” independent? Justify your answer. These events are not independent. There are several acceptable ways to show this P (5H ∩ B chosen) = ( . 5)( . 8)...
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  ## This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.
  
  ### Page1 / 4
  
  fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz#2 3:40...
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a solution set for a STAT 230 quiz from Fall 2006. It contains solutions to a math question involving probability calculations with two different coins. The document includes parts (a), (b), and (c) of the question, each with a detailed solution. The question is about calculating the probability of getting 5 consecutive heads, determining the probability that a specific coin was chosen given 5 consecutive heads, and assessing the independence of the events "Coin B chosen" and "5 consecutive heads."
  
  Label: question-and-answer