If you roll a pair of dice, what is the

auskunftsgkp

auskunftsgkp

Answered question

2022-02-13

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 & Explanation

Amiya Wolf

Amiya Wolf

Beginner2022-02-14Added 11 answers

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(AB)=P(A)+P(B)P(AB)
|Ω|=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)=1036
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)=1836
Event AB is "rolling a single 3 and an odd sum", so
AB={(3,2),(3,4),(3,6),(2,3),(4,3),(6,3)}
|AB|=6
P(AB)=636
Now we can use the first formula:
P(AB)=1036+1836636=2236=1118

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