$\underline{\mathbf {Answer:}}$ $\mathbf B$
$\underline{\mathbf{Explanation:}}$
This question is a combination of both conditional and total probability.
P(different outcomes | given at least one head has occurred)
$=\large{\frac{\text {P(different outcome)}\cap \mathrm P\text {(at least one head)}}{\text {P(at least one head)}} = \mathrm{\frac{p_1(1-p_2)+p_2(1-p_1)}{p_1(1-p_2)+p_2(1-p_1)+p_1p_2}}}$
which can be further simplified to
$=\mathrm{ \Large{\frac{(p_1+p_2) - 2p_1p_2}{(p_1+p_2)-p_1p_2}}}$
$\therefore \mathbf B$ is the correct option.