Question

Say if the following pairs of events should be modeled as independent or dependent. Explain your reasoning.

(a) We choose a voter at random (all voters equally likely) from Bloomington and let A be the event that the voter thinks the mayor is doing a good job and B be the event that the voter thinks the police chief is doing a good job.

(b) Two people are selected at random from Bloomington and let A be the event that the first person approves of the mayor, while B is the event that the 2nd person approves of the mayor.

(c) Flip a coin and let A be the event that the coin is heads and B be the event that the coin is tails.

(d) 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.”

Answer 1

Answer:

Given that:

(a) We choose a voter at random (all voters equally likely) from Bloomington and let A be the event that the voter thinks the mayor is doing a good job and B be the event that the voter thinks the police chief is doing a good job.

We choose a voter at random (all voters equally likely) from Bloomington. Let A be the event that the voter favours the mayor, and B be the event that the voter favours the police chief.

- Here, we are considering a single voter at random. Thus, he can choose either A or B. Thus, these are dependent events (As if a person favours mayor he can not favour police chief and vice versa)

b) Two people are selected at random from Bloomington and let A be the event that the first person approves of the mayor, while B is the event that the 2nd person approves of the mayor.

Two people are selected at random from Bloomington. Let A be the event that the first person favours the mayor, while B is the event that the 2nd person favours the mayor.

- Here. two different people are assigned to two events. Thus, these are independent events. (As both are free to choose what they want and it wont impact the other)

(c) Flip a coin and let A be the event that the coin is heads and B be the event that the coin is tails.

Flip a coin and let A be the event that the coin is heads, and B be the event that the coin is tails.

- These are dependent events (As a coin can either show head or tail, But if it is heads it can't be tails and vice versa)

(d) 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.”

A person is selected at random from Bloomington. Let A be the event that the person likes the movie "The Incredibles", while B is the event that the person likes "The Incredibles 2."

- These are independent events (Even though the person is same the choice of the movie solely depends on the person and should be independent