In a single throw of two dice, find
Question:

In a single throw of two dice, find P (a total greater than 8)

Solution:

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no. of Desired outcomes }}{\text { Total no. of outcomes }}$

Total outcomes are $(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$,

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

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

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

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

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

Desired outcomes are $(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)$

Total no. of outcomes are 36 and desired outcomes are 10

Therefore, probability of getting total greater than $8=\frac{10}{36}$

$=\frac{5}{18}$

Conclusion: Probability of getting total greater than 8, when two dice are rolled is $\frac{5}{18}$