Mathematics problem written explanation of answer

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Apr 8th, 2015

1. The sample space S of two dice is shown below.

S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
  (2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
  (3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
  (4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
  (5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
  (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }

so total no: of events in sample space =36 =n(S)


2. Let E be the event "sum greater than 7 ".

  Possible outcomes for sum greater than 7 : E = {(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}

  No: of Possible outcomes for sum greater than 7,n(E) = 15

 Possible outcomes for sum less than 7 : F = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2),(5,1)}

  No: of Possible outcomes for sum less than 7 = 15



3.  Probability P(E) FOR SUM GREATER THAN 7  = n(E) / n(S) = 15 / 36

  Probability P(E) FOR SUM LESS THAN 7  = n(F) / n(S) = 15 / 36

Please let me know if you have any questions and best me if you are satisfactory.

Apr 8th, 2015

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