Question

The following probability model shows the distribution of the most-popular-selling Girl Scout Cookies ® .

Cookie Type	Probability
Thin Mints	0.27
Samoas/Caramel deLites	0.21
Peanut Butter Patties/Tagalongs	0.17
Peanut Butter Sandwiches/ Do-is-dos	0.15
Shortbread/Trefoils	0.12
Other varieties	0.08

(a) Verify that this is a probability model. If a girl scout is selling cookies to people who randomly enter a shopping mall, what is the probability that the next box sold will be Peanut Butter Patties ® / Tagalongs™ or Peanut Butter Sandwich/Do-si-dos™?

(b) If a girl scout is selling cookies to people who randomly enter a shopping mall, what is the probability that the next box sold will be Thin Mints, Samoas ® /Caramel deLites™, or Shortbread/Trefoils?

(c) What is the probability that the next box sold will not be Thin Mints?

Answer 1

Cookie Type Thin Mints Samoas/Caramel delites Peanut Butter Patties/Tagalongs Peanut Butter Sandwiches/ Do-is-dos Shortbread/Trefoils Other varieties Probability 0.27 0.21 0.17 0.15 0.12 0.08 Total

a)   To verify that this is a probability model,          

• the sum of all probabilities should be equal to 1          
•    and each probability should be positive and less than or equal to 1          

   We can see that

•      the sum of all probabilities is equal to 1          
•    the probabilities are positive and less than 1          

   Hence, this is a probability model          
   Let           
   A: event that next box sold is Peanut Butter Patties ® / Tagalongs™          
   B: event that next box sold is Peanut Butter Sandwich/Do-si-dos™          
   From the given probabilities          
   P(A) = 0.17          
   P(B) = 0.15          
   To find P(next box sold will be Peanut Butter Patties ® / Tagalongs™ or Peanut Butter Sandwich/Do-si-dos™)          
   that is to find P(A OR B)          
   Since next box sold is 1 box it can be only one of the given types          
   Hence A and B are mutually exclusive          
   Hence,          
   P(A OR B) = P(A) + P(B)          
                        = 0.17 + 0.15          
                       = 0.32          
   P(next box sold will be Peanut Butter Patties ® / Tagalongs™ or Peanut Butter Sandwich/Do-si-dos™) = 0.32          
              
b)   Let           
   A: event that next box sold is Thin Mints          
   B: event that next box sold is Samoas/Caramel deLites          
   C: event that next box sold is Shortbread/Trefoils          
   From the given probabilities          
   P(A) = 0.27          
   P(B) = 0.21          
   P(C ) = 0.12          
   To find P(next box sold will be Thin Mints, Samoas ® /Caramel deLites™, or Shortbread/Trefoils)          
   that is to find P(A OR B OR C)          
   Since next box sold is 1 box it can be only one of the given types          
   Hence A, B and C are mutually exclusive          
   Hence,          
   P(A OR B OR C) = P(A) + P(B) + P(C )          
                        = 0.27 + 0.21 + 0.12          
                       = 0.6          
   P(next box sold will be Thin Mints, Samoas ® /Caramel deLites™, or Shortbread/Trefoils) = 0.6          
              
c)   Let           
   A: event that next box sold is Thin Mints          
   A' : event that next box sold is not Thin Mints          
   From the given probabilities          
   P(A) = 0.27          
   Hence,          
   P(A') = 1 - 0.27          
              = 0.73          
   P(next box sold will not be Thin Mints) = 0.73