SOLUTION: 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 proba

Algebra ->  Probability-and-statistics -> SOLUTION: 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 proba      Log On


   

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?
Found 3 solutions by Edwin McCravy, ikleyn, AnlytcPhil:
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
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?
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∙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

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
I have a question to Edwin. 

    Let suppose that 40 of 120 goldfish in the tank have a long fin, and 30 totally different of 120 goldfish have a long tail 

    (two non-intersecting subsets).  Then the conditions of the problem will be satisfied, but the probability under the question 

     will be 0 (zero, ZERO).



    Hence, something is wrong EITHER in the problem formulation OR in the Edwin' solution,  OR  in BOTH.



    The question is: WHAT IS WRONG ?


I think that these phrases  "every third goldfish has long fin"  and  "every fourth goldfish has a long tail"
are good as figures of speech,  but do not work  (have no a unique meaning)  in the formulation of the given Math problem.



Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
I took it that the fish are numbered 1 through 120.  I agree that

it is highly unusual that goldfish in a tank would be numbered like 

that, but then, there is no rule that says word problems in algebra

must be practical.  I agree that the problem could be worded better.

:)   Edwin (AnlytcPhil is my alias)