In$$Drosophila$,$ the normal $($wild$-$type$)$ body color is gray. A recessive allele for a particular autosomal gene results in a$$purple$$body color $($p$).$ A recessive allele for a different gene on the same chromosome results in a$$wingless$$fly $($w$).$ The two genetic loci are only $12$ MU apart. A true$-$breeding purple fly with normal wings is crossed with a true$-$breeding gray fly with no wings, all of the F$1$ offspring are gray with normal wings. If an F$1$ offspring with PW on one chromosome and pw on the other chromosome is mated with a purple fly that is heterozygous with wings, is there a possibility of having a wingless purple offspring?

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Yes

No

Can't be determined