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? if we use random number generator ranging from 1-10 and assign 1-4 as the prize and 5-10 as no prize, what is the best way to perform the simulation?

Solution:

Number of OatyPop cereal boxes Which contains a prize= 40 %

Number of OatyPop cereal boxes Which does not  contains a prize=100%- 40 %= 60%

Probability that Hannah only has to buy 3 or less boxes before getting a prize= S + F S + F F S =  40 %+ 60 %×  40 % +  60 % ×60 %× 40 %

        = 0.40 +0.24 + 0.144

         = 0.788

(b): If we use random number generator ranging from 1-10 and assign 1-4 as the prize and 5-10 as no prize, the best way to perform the simulation is:

Option(A): Keep track of how many tries it takes before you see a 1,2,3,or 4.These represent the number of purchases it will take to get a prize.Repeat this 150 times.

Why this simulation is preferred because we have created the table such that getting  number from [1-4] means winning a prize. So , we are not sure that only in 3 tries we will get a success, it takes more than 3 . So, success means either a number from [1-4], and each number has probability of if 150 trials will be performed.

whats the