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Each of the following problems consists of a question and the statements labelled $(1)$ and $(2)$. You must decide whether the data given for the statements are sufficient to answer the questions.

A fish tanks contains a number of fish, including $5$ Fantails. If two fish are selected from the tank at random, what is the probability that both will be Fantails?

1. The probability that the first fish chosen will be Fantail is $\frac{1}{2}$.
2. The probability that the second fish chosen will be Fantail is $\frac{4}{9}$.

1. Statement $(1)$ ALONE is sufficient, but statement $(2)$ alone is not sufficient.
2. Statement $(2)$ ALONE is sufficient, but statement $(1)$ alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
4. EACH statement ALONE is sufficient.