Question

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?

Answer 1

The probability is: `11/18`

Explanation:

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`