Given: A standard number cube is tossed
To determine: The P(even or prime)
Solution
Step 1: Write the element of the sample space
[tex]\begin{gathered} S=\mleft\lbrace1,2,3,4,5,6\mright\rbrace \\ n(S)=6 \end{gathered}[/tex]Step 2: Write the element of even
[tex]\begin{gathered} evennumber=\mleft\lbrace_{}2,4,6\mright\rbrace \\ n(\text{even)}=3 \end{gathered}[/tex]Step 3: Write the elemt of prime
[tex]\begin{gathered} prime\text{ number=}\mleft\lbrace2,3,5\mright\rbrace \\ n(prime\text{)}=3 \end{gathered}[/tex]Step 4: Write element of even and prime
[tex](\text{odd}\cap even)=\mleft\lbrace2\mright\rbrace[/tex]Step 5: Find the P(even or prime)
[tex]P_{(\text{even or odd)}}=P(even)+P(odd)-P(odd\cap even)[/tex][tex]\begin{gathered} P(\text{even)}=\frac{3}{6} \\ P(\text{prime)}=\frac{3}{6} \\ P(\text{even }\cap prime)=\frac{3}{6}+\frac{3}{6}-\frac{1}{6} \\ P(\text{even }\cap prime)=\frac{3+3-1}{6} \\ P(\text{even }\cap prime)=\frac{5}{6} \end{gathered}[/tex]Hence, the probability of even and odd is 5/6
