<s>[INST] Probability that minimum of two numbers is less than 4 Suppose I have to choose two numbers from set $$S=\{1,2,3,4,5,6 \}$$ without a replacement , then what is the probability that minimum of two is less than $4$?
I made two groups for this problem $A= \{1,2,3 \}$ and $B=\{4,5,6 \}$
.There are two possibilities , either both are from $A$ or one from $A$ and one from $B$ to satisfy our requirement. Hence
$$P(E)=\frac{3}{6}.\frac{2}{5} + \frac{3}{6}.\frac{3}{5}$$
but answer is incorrect. Help?
 [/INST] The error with your approach is that "One from $A$ and one from $B$" has two ways of happening: $A$ then $B$, or $B$ then $A$. So you need to multiply your calculation of this case by 2.
$$P(E) = \frac{3}{6} \cdot \frac{2}{5} + 2 \cdot \frac{3}{6} \cdot \frac{3}{5} = \frac{4}{5}$$
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