Question 162966
<pre><font size = 4 color = "indigo"><b>52 people answered yes and 77 answered no.  So the total number
of people answering the question was 52+77 or 129 people in the 
group. 52 people of the 129 answered yes, so

{{{P(Y) = 52/129}}}

5 males answered yes and 11 answer no.  So there were 5+11 or 16 
males in the group, so

{{{P(M) = 16/129}}}

Of the 52 people who answered yes to the question, 5 were male. 
These 5 were the only group members of the 129 who answered yes 
AND were males, so

{{{P(Y_and_M) = 5/129}}}

The we use the "sieve" formula:

{{{P(Y_or_M) = P(Y) + P(M) - P(Y_and_M)}}}

{{{P(Y_or_M) = 52/129+16/129-5/129}}}

{{{P(Y_or_M)=63/129}}}

{{{P(Y_or_M)=21/43}}}

{{{P(Y_or_M)=.488372093}}}

That's choice a.

Edwin</pre>