Answer to Question #162412 in Statistics and Probability for Nomhle Lukashe

Question

A breakfast cereal manufacturer packs one of five pictures (A, B, C, D, E) in each box of cereal. If you buy two boxes, what is the sample space for the random experiment whose outcome is the two pictures in the boxes? 2. A small town has three grocery stores (Choppies, Bakgatla and SaveRite). Four ladies living in this town each randomly and independently pick a store in which to shop. Give the sample space of the experiment which consists of the selection of the stores by the ladies. Then define the events: A: all the ladies choose Choppies B: half of the ladies choose Choppies and half choose Bakgatla C: all the stores are chosen by at least one lady.

Answer 1

(i) There are five Pictures $(A,B,C,D,E)$ and Manufacturers Pack two boxes.

SO The sample space are-

$(A,A),(A,B),(A,C),(A,D),(A,E)\\(B,A),(B,B),(B,C),(B,D),(B,E)\\(C,A),(C,B),(C,C),(C,D),(C,E)\\(D,A),(D,B),(D,C),(D,D),(D,E)\\(E,A),(E,B),(E,C),(E,D),(E,E)$

(ii) There are 3 grocery shop and 4 ladies

Each lady can select the shop Having sample space all three shops

Sample space-

(Choppies, Bakgatla ,SaveRite, choppies),(Choppies, Bakgatla and SaveRite,Bakgatla),(Choppies, Bakgatla and SaveRite, SaveRite),......., (Bakgatla, choppies, saverite, saverite)

A:All the Ladies choose choppies

Total number of favourable outcomes=$^4C_{1}=4$

B:Half of ladies choose choppies and half chooseBakgatla

Total number of favourable outcomes=$^2C_{1}\times ^2C_1=2\times 2=4$

C:All the stores are choosen by at least one lady

Total number of favourable outcomes=$^4C_{3}=4$