Question

Two dice are rolled together. Find the probability of getting a total of at least 10.

Answer 1

n(S) = 36 i.e.

(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)

In throwing a dice, total possible outcomes = {1, 2, 3, 4, 5, 6} 

n(S) = 6 

For two dice, n(S) = 6 × 6 = 36 

E = event of getting a total of at least 10 = {(4, 6),(5, 5),(5, 6),(6, 4),(6, 5),(6, 6)} 

n(E) = 6 

Probability of getting a total of at least 10 = `(n(E))/(n(S)) = 6/36 = 1/6`