ROLL A PAIR OF DICE

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ROLL A PAIR OF DICE AND ADD THE NUMBERS

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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. - PowerPoint PPT Presentation

Transcript of ROLL A PAIR OF DICE

Page 1: ROLL A PAIR OF DICE

ROLL A PAIR OF DICE

AND ADD THE NUMBERS

Page 2: ROLL A PAIR OF DICE

Possible Outcomes:

(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)

There are 6 x 6 = 36 equally likely

Page 3: ROLL A PAIR OF DICE

A more compact sample space might list only the possible sums.

These outcomes are not equiprobable and must be weighted as follows:

Page 4: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

6611 2112

6556

41322314

63544536

312213

645546

615243342516

5142332415

6253443526

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

Page 5: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

T = the event the sum is a multiple of 3

T = { 3, 6, 9, 12 } 2/36 5/36 4/36 1/36

P(T) = 2/36 + 5/36 + 4/36 + 1/36 = 12/36

Page 6: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

E = the event the sum is greater than 8

E = { 9, 10, 11, 12 } 4/36 3/36 2/36 1/36

P(E) = 4/36 + 3/36 + 2/36 + 1/36 = 10/36

Page 7: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

T = the event the sum is a multiple of 3

T = { 3, 6, 9, 12 } P(T) = 12/36 2/36 5/36 4/36 1/36

E = the event the sum is greater than 8

E = { 9, 10, 11, 12 } P(E) = 10/36 4/36 3/36 2/36 1/36

Page 8: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

T = { 3, 6, 9, 12 }P(T) = 12/36

2/36 5/36 4/36 1/36E = { 9, 10, 11, 12 }P(E) = 10/36

4/36 3/36 2/36 1/36

T E= the event the sum is a multiple of 3 AND greater than 8 =

{ 9, 12 } P(T E) = 5/36

T E= the event the sum is a multiple of 3 OR greater than 8

P(T E) = P(T) + P(E) - P(T E)

= 12/36 + 10/36 - 5/36 = 17/36

Page 9: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36

T = { 3, 6, 9, 12 }P(T) = 12/36

2/36 5/36 4/36 1/36E = { 9, 10, 11, 12 }P(E) = 10/36

4/36 3/36 2/36 1/36

T E= the event the sum is a multiple of 3 AND greater than 8 =

{ 9, 12 } P(T E) = 5/36

T / E= the event the sum is a multiple of 3 IF greater than 8

P(T / E) = P(T E) = 5/36 = 5 P( E ) 10/36 10

Page 10: ROLL A PAIR OF DICE

{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

The SAMPLE SPACE =

1/36 1/362/36 2/366/365/36 5/364/36 4/363/36 3/36


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