PROBABILTY
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
favourable cases are (1, 3), (2, 2), (3, 1)
∴ No. of favourable outcomes
= 3
3
36
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.
favourable cases are (1, 5) , (2, 4), (3, 3), (4, 2), (5,1)
∴ No. of favourable outcomes = 5
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.