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ROLL A PAIR OF DICE

ROLL A PAIR OF DICE. AND ADD THE NUMBERS. There are 6 x 6 = 36 equally likely. Possible Outcomes:. A more compact sample space might list only the possible sums. These outcomes are not equiprobable and must be weighted as follows:. 2/36. 3/36. 4/36. 5/36. 5/36. 4/36. 3/36. 2/36.

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ROLL A PAIR OF DICE

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  1. ROLL A PAIR OF DICE AND ADD THE NUMBERS

  2. There are 6 x 6 = 36 equally likely Possible Outcomes:

  3. A more compact sample space might list only the possible sums. These outcomes are not equiprobable and must be weighted as follows:

  4. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 1 1 6 6 1 2 5 6 1 2 3 1 6 5 4 2 4 6 4 5 3 1 1 6 2 4 5 5 2 3 2 4 3 4 3 5 6 3 5 4 4 3 2 1 6 5 4 4 3 2 1 6 3 5 1 5 3 4 1 6 2 3 2 3 5 6 2 1 6 5 4 2 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36

  5. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36 T = the event the sum is a multiple of 3 2/36 5/36 4/36 1/36 T = { 3, 6, 9, 12 } P(T) = 2/36 + 5/36 + 4/36 + 1/36 = 12/36

  6. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36 E = the event the sum is greater than 8 4/36 3/36 2/36 1/36 E = { 9, 10, 11, 12 } P(E) = 4/36 + 3/36 + 2/36 + 1/36 =10/36

  7. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 E = the event the sum is greater than 8 T = the event the sum is a multiple of 3 2/36 5/36 4/36 1/36 4/36 3/36 2/36 1/36 T = { 3, 6, 9, 12 } P(T) = 12/36 E = { 9, 10, 11, 12 } P(E) = 10/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36

  8. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 4/36 3/36 2/36 1/36 2/36 5/36 4/36 1/36 T E= the event the sum is a multiple of 3ANDgreater than 8 = { 9, 12 }P(T E) = 5/36 T = { 3, 6, 9, 12 } P(T) = 12/36 E = { 9, 10, 11, 12 } P(E) = 10/36 T E= the event the sum is a multiple of 3ORgreater than 8 P(T E) = P(T) +P(E) - P(T E) = 12/36 + 10/36 - 5/36 = 17/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36

  9. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 4/36 3/36 2/36 1/36 2/36 5/36 4/36 1/36 E = { 9, 10, 11, 12 } P(E) = 10/36 T = { 3, 6, 9, 12 } P(T) = 12/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36 T E= the event the sum is a multiple of 3ANDgreater than 8 = { 9, 12 }P(T E) = 5/36 T /E= the event the sum is a multiple of 3IFgreater than 8 P(T /E) = P(T E) = 5/36 = 5 P( E ) 10/36 10

  10. 2/36 3/36 4/36 5/36 5/36 4/36 3/36 2/36 1/36 1/36 The SAMPLE SPACE = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 6/36

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