Question 544419
<pre>
Two ways to do it:  (1) The formula way and 
(2) the Venn Diagram-Algebra way
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(1) The formula way:

P(T' and G') = {{{3/25}}}

By DeMorgan's law,  T' and G' = (T or G)' , so

P[(T or G)'] = {{{3/25}}}

P(T or G) = 1 - {{{3/25}}} = {{{25/25}}} - {{{3/25}}} = {{{22/25}}}

P(T or G) = P(T) + P(G) - P(T and G)

{{{22/25}}} = {{{14/25}}} + {{{16/25}}} - P(T and G)

P(T and G) = {{{14/25}}} + {{{16/25}}} - {{{22/25}}}

P(T and G) = {{{8/25}}}
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(2) the Venn Diagram-Algebra way
 
{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-1.2,4,4), locate(-2,1.8,x), locate(1.5,1.7,z),
locate(-3.5,2.5,T), locate(-.2,1.7,y),
circle(-sqrt(2),sqrt(2),2),locate(3.5,2.5,G),
circle(sqrt(2),sqrt(2),2), locate(-3.5,-.7,3)
 )}}}


We have the system of equations:

x + y     = 14
    y + z = 16
x + y + z + 3 = 25

Solve that and get x = 6, y = 8, z = 8

So we have:

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-1.2,4,4), locate(-2,1.8,6), locate(1.5,1.7,8),
locate(-3.5,2.5,T), locate(-.2,1.7,8),
circle(-sqrt(2),sqrt(2),2),locate(3.5,2.5,G),
circle(sqrt(2),sqrt(2),2), locate(-3.5,-.7,3)
 )}}}

The one that play tennis and golf are in this part of the
Venn diagram, because it's part of both T and G:

{{{drawing(320,350,-4,4,-5,4,
 
 locate(-.2,1.7,8),
arc(-sqrt(2),sqrt(2),4,-4,315,405),arc(sqrt(2),sqrt(2),4,-4,135,225)
 )}}}

That's 8 out of 25 which is {{{8/25}}}

Edwin</pre>