Answer:
The probability that he will roll three vowels = [tex]\displaystyle\bf\frac{1}{108}[/tex]
Step-by-step explanation:
We can find the probability that he will roll three vowels by using the probability formula:
[tex]\boxed{P(A)=\frac{n(A)}{n(S)} }[/tex]
where:
Let:
A = rolling a vowel on Die #1
= {A, E}
n(A) = 2
n(S) = 6
[tex]\displaystyle P(A)=\frac{n(A)}{n(S)}[/tex]
[tex]\displaystyle P(A)=\frac{2}{6}[/tex]
[tex]\displaystyle P(A)=\frac{1}{3}[/tex]
Let:
B = rolling a vowel on Die #2
= {I}
n(B) = 1
n(S) = 6
[tex]\displaystyle P(B)=\frac{n(B)}{n(S)}[/tex]
[tex]\displaystyle P(B)=\frac{1}{6}[/tex]
Let:
C = rolling a vowel on Die #3
= {O}
n(C) = 1
n(S) = 6
[tex]\displaystyle P(C)=\frac{n(C)}{n(S)}[/tex]
[tex]\displaystyle P(C)=\frac{1}{6}[/tex]
Since event A, B, and C are independent events. Then the probability of rolling three vowel:
[tex]P=P(A)\times P(B)\times P(C)[/tex]
[tex]\displaystyle=\frac{1}{3} \times\frac{1}{6} \times\frac{1}{6}[/tex]
[tex]\displaystyle=\bf\frac{1}{108}[/tex]