Answer to Question #226938 in Statistics and Probability for Zee

Question

Consider rolling two dice once. Calculate the probability of the...
2.1.1 rolling a sum of 5 or even sum
2.1.2 rolling a sum of 7 or 6
2.1.3 rolling a sum of 10 or an odd sum

Answer 1

Solution:

n(S) = 36

2.1.1:

Let E be an event of rolling a sum of 5 or even sum.

E = {(1,4),(4,1),(2,3),(3,2),(1,1),(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,5),(4,2),(4,4),(4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)}

n(E)=21

P(E) = $\dfrac{21}{36}=\dfrac{7}{12}$

2.1.2:

Let F be an event of rolling a sum of 7 or 6.

F = {(1,5),(5,1),(2,4),(4,2),(3,3),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)}

n(F) = 11

P(F) = $\dfrac{11}{36}$

2.1.3:

Let G be an event of rolling a sum of 10 or an odd sum.

G = {(4,6),(5,5),(6,4),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,1),(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)}

n(G) = 21

P(G) = $\dfrac{21}{36}=\dfrac{7}{12}$