Answer to Question #210800 in Statistics and Probability for sadauna

Question

A small town has three grocery stores (1, 2 and 3). 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

Answer 1

Three grocery stores: $1,2,3.$

Four ladies.

$S=\{1111, 1112, 1121, ..., 3333\}, 3^4=81$ elementary events.

A: all ladies choose the store 1: $A=\{1111\}$

B: half the ladies choose the store 1 and half the ladies choose the store 2 :

$B=\{1122\}, \{1212\}, \{1221\}, \{2211\}, \{2121\},\{2112\}$

C: all the stores are chosen (by at least one lady):

$C=\{1231\}, \{1232\}, \{1233\}, \{1321\}, ...,\{3321\},$ $36$ elementary events.