If you roll a pair of dice, what is the probability of rolling either a single 3 or a sum that is an odd number?

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Answer 1 · 2015-11-06T23:49:02

The probability is: $11/18$

In this task we have to calculate the probability of sum of 2 events (i.e. rolling a single 3 or rolling an odd sum).

To do this we must use the following formula:

$P(AuuB)=P(A)+P(B)-P(AnnB)$

$|Omega|=36$

Event $A$ is "rolling a single 3", so:

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

$|A|=10$ , $P(A)=10/36$

Event $B$ is "rolling an odd sum", so:

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

$|B|=18$

$P(B)=18/36$

Event $AnnB$ is "rolling a single 3 and an odd sum", so

$AnnB={(3,2),(3,4),(3,6),(2,3),(4,3),(6,3)}$

$|AnnB|=6$

$P(AnnB)=6/36$

Now we can use the first formula:

$P(AuuB)=10/36+18/36-6/36=22/36=11/18$