Question

40% of OatyPop cereal boxes contain a prize. Hanna plans to keep buying cereal until she gets a prize. What is the probability that Hannah only has to buy 3 or less boxes before getting a prize? Use the simulation to find the probability

Answer 1

Answer: 86%

Hope this helps!!!

Answer 2

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

=
`(40)/(100)+(40* 60)/(10000)+(60 * 60 *40)/(1000000)+.....{\text{infinity}}\\\\ (40)/(100)*[((60)/(100))/(1-(60)/(100))]\\\\ =(60)/(100)=0.6` 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)

=
`(40)/(100)+(60)/(100)*(40)/(100)+(60)/(100)*(60)/(100)*(40)/(100)+(60)/(100)*(60)/(100)*(60)/(100)*(40)/(100)\\\\=0.4+0.24+0.144+0.864\\\\ =0.8704`= 87.04 %