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PROBABILITY

  • Finding Probability : Sum based on 2 Dice contd...

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  1. When the sum on 2 dice is 9,

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

∴ No. of favourable outcomes = 4

 

 

4

36

3

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),

(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.

  1. When the sum on 2 dice is 10,

favourable cases are (4, 6), (5, 5), (6, 4)

∴ No. of favourable outcomes = 3

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Sol.

  1. When the sum on 2 dice is 11,

favourable cases are (5, 6), (6, 5)

∴ No. of favourable outcomes = 2

 

(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

2

36

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

1

36

2

36

5

36

6

36

4

36

3

36

5

36

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Do you agree with this argument? Justify your answer.

Sol.

No. The eleven sums are not equally likely

 

  1. A student argues that ‘there are 11 possible outcomes 2,3,4,5, 6, 7, 8,9,10,11 and 12.

Therefore, each of them has probability

1

11

(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),