text: # Solving Probability
  
  Updated on November 17, 2008
  
  SOLVING PROBABILITY
  
  Classical Definition of PROBABILITY
  
  If an experiment can result in a certain number of possible outcomes N, then the probability of the occurrence of an event A is:
  
  number of occurrences of A
  
  ==================================-
  
  Total number of possible outcomes
  
  Example (1) :
  
  A fair coin is tossed three times. Find the probability of getting at least . two heads.
  
  Solution :
  
  Let A = be the event of getting at least two heads
  
  Let S = Sample Space which refers to the total number of possible outcomes
  
  S = ( HHH, HHT, HTH, THH, HTT,THT,TTH,TTT ) = 8
  
  A = ( HHT, HTH, THH, HHH ) = 4
  
  P(A) = 4/8 = 1/2
  
  The probability of getting at least two heads when a coin is tossed three times
  
  Is ½.
  
  Example ( 2 ) :
  
  To form a committee, four people are to be selected from a group of five
  
  doctors and five lawyers. Find the probability of including two doctors in the
  
  committee.
  
  First find the Sample Space which is total number of possible committees
  
  consisting of four members selected from ten members.
  
  Sample Space = 10 C 4 = 10 !/ (10 - 4)! 4! = 210
  
  Next find the number of possible committees formed consisting of two doctors.
  
  Let this be n.
  
  n = 5 C 2 * 5 C 2 = 5! / 3! 2! * 5!/3! 2!
  
  = 10 * 10 = 100
  
  P(A) = n / Sample Space = 100 / 210 = 10/ 21
  
  The probability of including two doctors in the committee is 10/21.
  
  45
  
  3
  
  3
  
  10
  
  26
  
  0
  
  working
explanation: The document provides examples of solving probability problems. It includes two detailed examples with questions and corresponding solutions.
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distilabel_metadata.content: # Solving Probability
  
  Updated on November 17, 2008
  
  SOLVING PROBABILITY
  
  Classical Definition of PROBABILITY
  
  If an experiment can result in a certain number of possible outcomes N, then the probability of the occurrence of an event A is:
  
  number of occurrences of A
  
  ==================================-
  
  Total number of possible outcomes
  
  Example (1) :
  
  A fair coin is tossed three times. Find the probability of getting at least . two heads.
  
  Solution :
  
  Let A = be the event of getting at least two heads
  
  Let S = Sample Space which refers to the total number of possible outcomes
  
  S = ( HHH, HHT, HTH, THH, HTT,THT,TTH,TTT ) = 8
  
  A = ( HHT, HTH, THH, HHH ) = 4
  
  P(A) = 4/8 = 1/2
  
  The probability of getting at least two heads when a coin is tossed three times
  
  Is ½.
  
  Example ( 2 ) :
  
  To form a committee, four people are to be selected from a group of five
  
  doctors and five lawyers. Find the probability of including two doctors in the
  
  committee.
  
  First find the Sample Space which is total number of possible committees
  
  consisting of four members selected from ten members.
  
  Sample Space = 10 C 4 = 10 !/ (10 - 4)! 4! = 210
  
  Next find the number of possible committees formed consisting of two doctors.
  
  Let this be n.
  
  n = 5 C 2 * 5 C 2 = 5! / 3! 2! * 5!/3! 2!
  
  = 10 * 10 = 100
  
  P(A) = n / Sample Space = 100 / 210 = 10/ 21
  
  The probability of including two doctors in the committee is 10/21.
  
  45
  
  3
  
  3
  
  10
  
  26
  
  0
  
  working
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides examples of solving probability problems. It includes two detailed examples with questions and corresponding solutions. 
  
  Label: multiple-question-and-answer