Which of the following sample spaces are uniform?
- {land,sea} for a random point on a globe
- {odd, even} for a random integer: $z \in \{1,2, \ldots ,100 \}$
- {leap year, non-leap year} for a random year before $2019$
- {two heads, two tails, one head and one tail} when flipping two fair coins
- {distance to origin} for a random point in $\{−3, −1, 1, 3\} \times \{−4, −2, 2, 4\}$
I know that 2 is uniform as they have the same probability.
I like to think that 1 is also uniform as picking a random point on the globe will always have the same probability, the same with the leap year. But they do not have the same probability of occurring so I think they aren't uniform spaces.
I think not 4 as the probability of having two heads/tails varies from one head and one tail. However, a fair coin is uniform.
The last bit confuses me.
Your answers for parts $1$ and $3$ are not correct.
The globe has more water area than land area.
There are also more normal years than leap years.
The last one is uniform because you have four possible results and each one occurs exactly four times.
The possible outcomes are $$\sqrt 5, \sqrt {17}, 5,\sqrt {13}$$