Solution:
Amount of Oatypop that contains the prize = 40%
Amount of Oatypop which doesn't contain the prize = (100-40)=60%
Probability that hannah will win a prize
= S +F S +F F S+FF F S+FF F F S+.....till infinity.where F= Failure,S= Success
= [tex]\frac{40}{100}+\frac{40\times 60}{10000}+\frac{60 \times 60 \times40}{1000000}+.....{\text{infinity}}\\\\ \frac{40}{100}\times[\frac{\frac{60}{100}}{1-\frac{60}{100}}]\\\\ =\frac{60}{100}=0.6[/tex] or 60%
Probability that Hannah only has to buy 3 or less boxes before getting a prize= (S) and ( F S) and (FF S) and (F F F S)
= [tex]\frac{40}{100}+\frac{60}{100}\times\frac{40}{100}+\frac{60}{100}\times\frac{60}{100}\times\frac{40}{100}+\frac{60}{100}\times\frac{60}{100}\times\frac{60}{100}\times\frac{40}{100}\\\\=0.4+0.24+0.144+0.864\\\\ =0.8704[/tex]= 87.04 %
