From the numbers 3 to 12 inclusive two numbers are chosen at random.?

a) What is the cardinality of the sample space?


b) List the event in which number is a factor of the other number and find its cardinality.


c) List the event in which the sum of the numbers is 15.


d)List the event in which the sum of the numbers is 15 and one number is a factor of the other number.

From the numbers 3 to 12 inclusive two numbers are chosen at random.?
A)What is the cardinality of the sample space?


The sample space O={3,4,5,6,7,8,9,10,11,12} and its C is 10 as it has 10 items


B)These are the pairs:


(3,6),(3,9),(3,12),(4,8),(4,12),(5,10)...


So A={(3,6),(3,9),(3,12),(4,8),(4,12),(5,10... and its C is 7


C)These are the pairs:


(3,12),(4,11),(5,10),(6,9),(7,8)


So B={(3,12),(4,11),(5,10),(6,9),(7,8)} and its C is 5


D)C=A AND B={(3,12),(5,10)} and its C is 2





Notes:


1)You haven't defined whether both numbers can be the same. In this case A also has {(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,... and its C is +12


2)You haven't defined whether the pairs are ordered, meaning if the incident of choosing ie (3,4) is not treated as if choosing (4,3). In this case A also has {(6,3),(9,3),(12,3),(8,4),(12,4),(10,5),... and its C is +7, B also has {(12,3),(11,4),(10,5),(9,6),(8,7)} and its C is +5 and C also has {(12,3),(10,5)} and its C is +2





Note that none, either or both of those notes can be defined.