In a single throw of two dice, find the probability of getting the sum

1.	In a single throw of two dice, find the probability of getting the sum of numbers appearing on the two dice.(i) greater than 8 (ii) Less than or equal to 12 (iii) equal to 7 (iv) divisible by 3 or 4
Answer» 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) (i) (6,3),(6,4),(6,5),(6,6),(3,6),(4,5),(4,6),(5,4),(5,5),(5,6) P (sum greater than 8) = 10/36 (ii) Less than or equal to 12 = ? Outcomes = All Outcomes have sum less than or equal to 12. P (sum Less than or equal to 12) = 36/36 = 1 (iii) Sum equal to 7 Outcomes = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 P (sum equal to 7) = 6/36 (iv) Divisible by 3 or 4 Outcomes = (1,2),(1,3),(1,5),(2,1)(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(3,6),(4,2),(4,4),(4,5),(5,1),(5,3),(5,4),(6,2),(6,3),(6,6) P(divisible by 3 or 4) = 20/36

In a single throw of two dice, find the probability of getting the sum of numbers appearing on the two dice.(i) greater than 8 (ii) Less than or equal to 12 (iii) equal to 7 (iv) divisible by 3 or 4

Answer»

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)

(i) (6,3),(6,4),(6,5),(6,6),(3,6),(4,5),(4,6),(5,4),(5,5),(5,6)

P (sum greater than 8) = 10/36

(ii) Less than or equal to 12 = ?

Outcomes = All Outcomes have sum less than or equal to 12.

P (sum Less than or equal to 12) = 36/36 = 1

(iii) Sum equal to 7

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

P (sum equal to 7) = 6/36

(iv) Divisible by 3 or 4

Outcomes =

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

P(divisible by 3 or 4) = 20/36