# In a single throw of two dice, determine the probability of not getting

Question:

In a single throw of two dice, determine the probability of not getting the same number on the two dice.

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 all outcomes except $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

Total no. of outcomes are 36 and desired outcomes are 30

probability of not getting same number $=\frac{30}{36}$

$=\frac{5}{6}$

Conclusion: Probability of not getting the same number on the two dice is $\frac{5}{6}$