Problem 1
S = sample space = set of all possible outcomes
S = set of positive factors of 72
S = {1,2,3,4,6,8,9,12,18,24,36,72}
n(S) = number of items in sample space
n(S) = 12
E = event space = set of outcomes we want to happen
E = set of factors of 72 such that they are less than 10
E = {1,2,3,4,6,8,9}
n(S) = number of items in event space
n(S) = 7
P(E) = probability get a value in set E (that is also in set S as well)
P(E) = probability we get a positive factor of 72 that is less than 10
P(E) = n(E)/n(S)
P(E) = 7/12
<h3>Answer: 7/12</h3>
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Problem 2
![\begin{array}{ccl}S & = & \text{Sample Space}\\\\S & = & \{\\ & & ~~DAB, DAC, DAE, DAF, DAG, DAH\\ & & ~~DBA, DCA, DEA, DFA, DGA, DHA\\ & & \}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccl%7DS%20%20%26%20%3D%20%20%26%20%5Ctext%7BSample%20Space%7D%5C%5C%5C%5CS%20%26%20%3D%20%26%20%5C%7B%5C%5C%20%26%20%20%20%26%20~~DAB%2C%20DAC%2C%20DAE%2C%20DAF%2C%20DAG%2C%20DAH%5C%5C%20%26%20%20%26%20~~DBA%2C%20DCA%2C%20DEA%2C%20DFA%2C%20DGA%2C%20DHA%5C%5C%20%26%20%20%26%20%5C%7D%5Cend%7Barray%7D)
n(S) = 12
E = event space
E = {DCA}
n(E) = 1
P(E) = probability we get an item in set S that is in set E also
P(E) = probability we get DCA from set S listed above
P(E) = n(E)/n(S)
P(E) = 1/12
<h3>Answer: 1/12</h3>