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?

The probability $P$(minimum is $ \lt 4)$ is 
$1 - P($ minimum is $\geq 4 ) = 1 - P($ both choices are from $A$ $)$.
The probability that both choices are from $A$ is $\frac{3}{6} \cdot \frac{2}{5}=\frac{1}{5}$.
Thus, the probability you're looking for is $\frac{4}{5}$.
