<s>[INST] If we take 5 shots with a basketball, what's the probability that you make 2 given you make at least 1? Probability of making a shot is $\displaystyle \frac{3}{5}$.
So $2$ shots would be $\displaystyle \dbinom{5}{2} \left(\frac{3}{5}\right)^2 \left(\frac{2}{5}\right)^3$ right? 
 [/INST] To find the probability in question, you have to first check what the probability of making at least $1$ shot is, and also the probability of making exactly $2$ shots, and then divide the latter by the former. That is, the probability is $$\frac{\text{(probability of landing 2 shots)}}{\text{(probability of landing at least 1 shot)}}$$

Probability of landing at least $1$ shot:
This is the same as $1$ minus the probability of missing all $5$ shots. The answer, therefore, is $$1 - \left(\frac{2}{5}\right)^5$$

Probability of landing exactly $2$ shots:
This is the answer that you had, i.e. $$\dbinom{5}{2} \left(\frac{3}{5}\right)^2 \left(\frac{2}{5}\right)^3$$

Final answer:
$$\frac{\dbinom{5}{2} \left(\frac{3}{5}\right)^2 \left(\frac{2}{5}\right)^3}{1-\left(\frac{2}{5}\right)^5} = \boxed{\frac{240}{1031}}$$
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