A pair of dice is rolled. A possible event is rolling a sum that is a multiple of 5. What is the probability of the complement of this event?

The probability of the complement of this event is ##1/6##.

The possible probabilities of rolling pair of dices in order to get the sum of the events, a multiple of 5 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)}.##

So, in total there are ##36## observations.

Out of these, no. of observations in which sum is multiple of ##5## is ##6##.

So, let, ##P(E)## be the probability of finding the given condition.

So, ##P(E)=(n(E))/(n(S))##.

##:.P(E)=6/36=1/6##. (Answer).