Conditional Probability problem on single coin toss

Question

A fair coin is tossed 4 times. Provided that at least 2 heads occurred within the 4 tossings, what's the probability that at least one tail also occurred?

Answer 1

$$ \begin{array}{l} \begin{array}{cccc} H & H & H & H \end{array} \\ \left.\begin{array}{cccc} H & H & H & t \\ H & H & t & H \\ H & t & H & H \\ t & H & H & H \end{array} \right\} \text{ 3 heads in 4 tosses} \\ \left.\begin{array}{cccc} H & H & t & t \\ H & t & H & t \\ t & H & H & t \\ H & t & t & H \\ t & H & t & H \\ t & t & H & H \end{array} \right\} \text{ 2 heads in 4 tosses} \end{array} $$ There are $6$ ways to get $2$ heads and $4$ ways to get $3$ heads, and just one way to get $4$ heads. Thus $11$ ways to get at least $2$ heads. In $10$ of those $11$ ways, there is at least $1$ tail.