Answer:
a) Ω = { {Abby, Deborath}, {Abby, Mei-Ling}, {Abby, Sam}, {Abby,Roberto}, {Deborah, Mei-Ling}, {Deborah, Sam}, {Deborah, Roberto}, {Mei-Ling, Sam}, {Mei-Ling, Roberto}, {Sam, Roberto} }
b) 0.1
c) 0.4
d) 0.3
Step-by-step explanation:
a) The sample space must contain every possible combination of two names. Since we dont care about the <em>order</em> of the chosen names, we can describe every element of the sample space as a <em>subset</em> of 2 elements of the set {Abby, Deborah, Mei-Ling, Sam, Roberto}. That subset will represent the names of the chosen persons. With this in mind, we conclude that the sample space is
Ω = { {Abby, Deborath}, {Abby, Mei-Ling}, {Abby, Sam}, {Abby,Roberto}, {Deborah, Mei-Ling}, {Deborah, Sam}, {Deborah, Roberto}, {Mei-Ling, Sam}, {Mei-Ling, Roberto}, {Sam, Roberto} }
b) The cardinality of the sample space Ω is 10. Since all choices are <em>equally likely</em>, any choice will have probability 
, because the 10 of them combined must add up 1.
c) We need to find all possible choices that includes Mei-Ling, those will be our <em>favourable cases. </em>The amount of favourable cases must be divided to the total amount of cases (the cardinality of Ω) in order to obtain the probability of Mei-Ling being chosen. Mei-Ling is included on 4 choices (one for each of her partners), this means that she has a probability of 
to being chosen.
d) We have <em>3 favourable cases </em>,the choices {Abby, Deborah}, {Abby, Mei-Ling} and {Deborah, Mei-Ling}, which neither of them contain a man. By dividing that number to the total number of cases, we obtain a probability of 
that neither of the two men are chosen
