Answer:
the probability = [tex]\displaystyle\bf\frac{1}{9}[/tex]
Step-by-step explanation:
We can find the probability of rolling a sum of 5 using a pair of dice with the probability formula:
[tex]\boxed{P(A)=\frac{n(A)}{n(S)} }[/tex]
where:
- [tex]P(A)[/tex] = probability of event A
- [tex]n(A)[/tex] = number of outcomes of event A
- [tex]n(S)[/tex] = total number of all outcomes
Since each dice has 6 faces and 2 dice are rolled, therefore:
[tex]the\ total\ number\ of\ outcomes\ (n(S))= 6^2[/tex]
[tex]\bf n(S)=36[/tex]
Let A = event of rolling a sum of 5, then:
A = {(1,4), (2,3), (3,2), (4,1)}
[tex]\bf n(A)=4[/tex]
Using the probability formula:
[tex]\displaystyle P(A)=\frac{n(A)}{n(S)}[/tex]
[tex]\displaystyle=\frac{4}{36}[/tex]
[tex]\displaystyle =\bf\frac{1}{9}[/tex]
