Given:
Given that four far dice are thrown.
Required: Probability of getting an even number on each one.
Explanation:
The sample space is
[tex]S=\lbrace(x,y,z,w):\text{ x,y,z,w =1,2,3,4,5,6\textbraceright}[/tex]
The number of elements in the sample space is
[tex]\begin{gathered} n(S)=6\times6\times6\times6 \\ =6^4 \end{gathered}[/tex]
Let E be the event of getting even on each dice. Then
[tex]E=\lbrace(x,y,z,w);x,y,z,w=2,4,6\rbrace[/tex]
The number of elements in E is
[tex]\begin{gathered} n(E)=3\times3\times3\times3 \\ =3^4 \end{gathered}[/tex]
The probability of getting even on each dice is
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ =\frac{3^4}{6^4} \\ =\frac{3^4}{2^4\cdot3^4} \\ =\frac{1}{2^4} \\ =\frac{1}{16} \end{gathered}[/tex]
The second option is correct.
Final Answer: The probability of getting even on each dice is 1/16.
