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PROBABILTY

  • Finding Probability : Sum based on 2 Dice

2 of 4

Q. Two dice, one blue and one grey are thrown at the same time (i) Complete the following table :

When two dice are thrown,

Different possible outcomes are

Total number of possible outcomes = 36

(a) When the sum on 2 dice is 3,

favourable cases are

No. of favourable outcomes

Sol.

(1, 2), (2, 1)

= 2

Event ‘Sum

on 2 dice’

Probability

2 3 4 5 6 7 8 9 10 11 12

 

1

36

5

36

1

36

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

What is the smallest sum of the scores ?

1 + 1 = 2

What is the biggest sum of the scores ?

6 + 6 = 12

So sum of the scores will be between 2 & 12 including 2 and 12

(1,1)

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

2

36

2

3

4

5

6

7

8

9

10

11

12

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  1. When the sum on 2 dice is 4,

favourable cases are (1, 3), (2, 2), (3, 1)

No. of favourable outcomes

= 3

 

3

36

  1. When the sum on 2 dice is 5,

favourable cases are (1, 4) , (2, 3), (3, 2), (4, 1)

No. of favourable outcomes = 4

 

4

36

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

(1,1),

(2,1) (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

(1,1),

(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),

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

2

3

4

5

6

7

8

9

10

11

12

Q. Two dice, one blue and one grey are thrown at the same time (i) Complete the following table :

Event ‘Sum

on 2 dice’

Probability

2 3 4 5 6 7 8 9 10 11 12

1

36

5

36

1

36

2

36

Sol.

4 of 4

  1. When the sum on 2 dice is 6,

favourable cases are (1, 5) , (2, 4), (3, 3), (4, 2), (5,1)

No. of favourable outcomes = 5

 

  1. When the sum on 2 dice is 7,

favourable cases are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

No. of favourable outcomes = 6

 

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

(1,1),

(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)

(1,2),

(1,3),

(1,4),

(1,5),

(1,6),

2

3

4

5

6

7

8

9

10

11

12

3

36

4

36

Q. Two dice, one blue and one grey are thrown at the same time (i) Complete the following table :

Event ‘Sum

on 2 dice’

Probability

2 3 4 5 6 7 8 9 10 11 12

1

36

5

36

1

36

2

36

5

36

6

36

Sol.