In a single throw of two dice, determine the probability of not getting the same number on the two dice.
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 $\frac{5}{6}$