Let S = {1, 2, 3} be a sample space associated with an experiment.

Question

Let S = {1, 2, 3} be a sample space associated with an experiment.
a. List all possible events of this experiment. (Hint: There are 8.)
b. In how many events does outcome 3 occur?
c. In how many events does either outcome 2 or outcome 3 occur (or both)?

Answer 1

a) ∅ (the empty set or null set)

   {1,2,3} (S, the set itself)

   { 1 }

   { 2 }

   { 3 }

   { 1,2 }

   { 1,3 }

   { 2,3 }

 

b) 4

 

c) 6

Answer 2

For this sample space, it seems that any outcome can either occur or not. That means it could be that 1 occurs, but not 2 or 3; it could be that 1 and 3 occur, but not 2; or it could be that none of the three occur. So, the possible events are:

 

None occur

1 occurs

2 occurs

3 occurs

1 and 2 occur

1 and 3 occur

2 and 3 occur

1, 2, and 3 occur

 

Now, just count how many of the eight events include 3 occurring and how many include either 2 or 3 occurring.