We will use the following formula:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B).[/tex]
First, we compute the probability that we get a blue marble:
[tex]P(\text{Blue)}=\frac{6}{5+6}=\frac{6}{11}\text{.}[/tex]
Now, we compute the probability of getting an odd-numbered marble:
[tex]P(\text{odd-num)}=\frac{6}{11}\text{.}[/tex]
Finally, the probability that we draw a blue and odd-numbered marble is:
[tex]P(\text{blue and odd)=}\frac{3}{11}.[/tex]
Answer: The probability that the marble is blue or odd-numbered is:
[tex]\begin{gathered} P(\text{blue or odd)=P(blue)+P(odd-num)-P(blue and odd)=}\frac{6}{11}+\frac{6}{11}-\frac{3}{11}=\frac{9}{11}. \\ P(\text{blue or odd)}=\frac{9}{11}\text{.} \end{gathered}[/tex]
