Question 1118396
in a certain pet store, every third goldfish has long fin, and every fourth
goldfish has a long tail. if a fish is selected at a random from a tank of 120
fish, what is the probability that the fish will have long fins and a long tail?
<pre>
Fishes 3,6,9,12,...,120 have a long fin, 
i.e., fish numbered with multiples of 3.

Fishes 4,8,12,16,...,120 have a long tail.
i.e., fish numbered with multiples of 4.

The fish that are in both categories are fish
numberered with multiples of both 3 and 4, which
are multiples of 3&#8729;4, which is 12. So

Fishes 12,24,36,48,...,120 have both a long fin and
a long tail.

Dividing each of these 12,24,36,48,...,120 by 12
gives                   1, 2, 3, 4,..., 10

So 10 of the fish have both long fins and tails.

The probability that they have both is 

10 out of 120 or 10÷120 = 10/120 = 1/12

Edwin</pre>