I'm trying to make sure that my reasoning is correct for these problems.
Say if the following pairs of events should be modeled as independent or dependent. Explain your reasoning.
We choose a voter at random (all voters equally likely) from Bloomington and let A be the event that the voter votes to reelect the mayor and B be the event that the voter votes to reelect the police chief. (these are not mutually exclusive choices, . . . , a person could vote to reelect both, neither, etc.)
- Independent, because the first person voting on the mayor doesn't affect how the 2nd person votes on the police chief.
Two people are selected at random from Bloomington and let A be the event that the first person favors the mayor, while B is the event that the 2nd person favors the mayor.
- These two events should be modeled as independent because the people were picked at random as well as they their decisions don't affect the other's.
Flip a coin and let A be the event that the coin is heads and B be the event that the coin is tails.
- This event is independent because regardless of how many flip the coin or if you don't do the first coin flip the probability will always be 50%
A person is selected at random from Bloomington. A is the event that the person likes the movie “The Incredibles” while B is the event that the person likes “The Incredibles 2.”
- These variables share a dependent relationship due to the fact that the two items are closely related and if you liked the first one it changes how much you like the second.