There are nine possible outcomes:



(in cents):

25 and 25      x

25 and 100     x 

25 and 200 

100 and 25     x

100 and 100    x

100 and 200

200 and 25

200 and 100

200 and 200          



Only the four outcomes marked with an x add to less than 225 (= $2.25)



We can not say P(sum < 225) = 4/9, however, because not all the listed outcomes are equally likely.  Here are the probabilities for the marked outcomes:



25 and 25      1/15 

25 and 100     2/15

100 and 25     2/15

100 and 100    1/15

               ----

               6/15 =    or 40%









 

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