In case of multi-stage experiments, each element of the sample space can have more than two components.
See solution.
Practice makes perfect
We use a table to display two-dimensional data. If we have two-stage experiments we can present the sample space by listing the possible outcomes of the first stage in the columns and outcomes of the second stage in the rows. Let's consider an example of flipping a coin followed by rolling a die.
Let's present the sample space of this experiment using a table. We will have 2 columns — each representing one possible outcome of flipping a coin, and 6 rows — each representing a possible outcome of rolling a die.
Heads
Tails
1
(H,1)
(T,1)
2
(H,2)
(T,2)
3
(H,3)
(T,3)
4
(H,4)
(T,4)
5
(H,5)
(T,5)
6
(H,6)
(T,6)
Now, if we would like to perform a three-stage experiment we could not use a table to present the sample space. This is because the number of stages indicates the number of elements that each outcome is made of. Since a table is two-dimensional, we can only use it to show two-stage experiments.
