All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Firstly, the probability of picking a free gift is constant. Secondly, there is only two possible outcomes, i.e., the packets either contain a free gift or do no contain a free gift.

(ii)
$F~\sim~B(20, ~0.05 )$
$\mathrm{P}(F=1) = 0.377$

(iii)
$F~\sim~B(60, ~0.05 )$
Since $n$ is large, $np = 3 < 5, ~ F~\sim~\mathrm{Po}(3)$ approximately. $\mathrm{P}(F >ge 1) = 1 - \mathrm{P}(F \le 4) = 0.185$