Answer :
Let C and D be the set of people who prefer cats and dogs respectively.
According to the given problem,
[tex]\begin{gathered} n(C)=156 \\ n(D)=59 \\ n(none)=61 \end{gathered}[/tex]Note that mathematically, you can prefer one thing at a time. That means that none of the surveyed people will prefer cat and dog both,
[tex]n(C\cap D)=0[/tex]Then the total number of people surveyed is calculated as,
[tex]\begin{gathered} n(Total)=n(C)+n(D)+n(none) \\ n(Total)=156+59+61 \\ n(Total)=276 \end{gathered}[/tex]The probability of an event is given by,
[tex]\text{ Probability}=\frac{\text{ Number of favorable outcomes}}{\text{ Total number of outcomes}}[/tex]So the probability that a randomly chosen person will prefer dogs, is calculated as,
[tex]\begin{gathered} P(D)=\frac{n(D)}{n(Total)} \\ P(D)=\frac{59}{276} \end{gathered}[/tex]Thus, the corresponding probability is,
[tex]\frac{59}{276}[/tex]