Let S 3 6 15 be a sample space associated with an experimen

Let S = {3, 6, 15} be a sample space associated with an experiment.
(a) List all events of this experiment.
, {3}, {6}, {15}, {3, 6}, {3, 15}, {6, 15}, {3, 6, 15}

{3}, {6}, {15}, {3, 6}, {3, 15}, {6, 15}  

{3}, {6}, {15}, {3, 6}, {3, 15}, {6, 15}, {3, 6, 15}

, {3}, {6}, {15}, {3, 6}, {3, 15}, {6, 15}

{3, 6}, {3, 15}, {6, 15}, {3, 6, 15}

, {3, 6}, {3, 15}, {6, 15}, {3, 6, 15}

(b) How many subsets of S contain the number 15?  

? subsets

(c) How many subsets of S contain the number 6 or the number 15?

? subsets

Solution

Since there are three elements in the Set S

a) The number of events in this experiment will be equal to Powerset(a,b,c)

Powerset will contain 2^(n) sets=> 2^(3) = 8 events

, {3}, {6}, {15}, {3, 6}, {3, 15}, {6, 15}, {3, 6, 15}

b) The number of subset that contain 15 will be equal to

2^(3-1) = 2^2 = 4 subsets, since the 15th elements must be present hence we can discard half the sets which don\'t contain 15

c) The number of sets that contain 6 or 15

Number of sets that contain 6 or 15 = Sets formed by only the element 3 and phi

Hence the correct answer is 8 - 2 = 6 sets