Answer :
Given
A single die is rolled.
To find the probability of rolling an odd number or a number less than 6.
Explanation:
It is given that,
A single die is rolled.
Then, the sample space is,
[tex]\begin{gathered} S=\lbrace1,2,3,4,5,6\rbrace \\ n(S)=6 \end{gathered}[/tex]Let A be the event of getting an odd number.
Then,
[tex]\begin{gathered} A=\lbrace1,3,5\rbrace \\ n(A)=3 \end{gathered}[/tex]Let B be the event of getting a number less than 6.
Then,
[tex]\begin{gathered} B=\lbrace1,2,3,4,5\rbrace \\ n(B)=5 \end{gathered}[/tex]Also,
[tex]\begin{gathered} A\cap B=\lbrace1,3,5\rbrace \\ n(A\cap B)=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{n(A\cap B)}{n(S)} \\ =\frac{3}{6}+\frac{5}{6}-\frac{3}{6} \\ =\frac{3+5-3}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Hence, the answer is 5/6.
