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Should the following pairs of events be modeled as independent or dependent? Explain your reasoning. (a)...

Should the following pairs of events be modeled as independent or dependent? Explain your reasoning.

(a) We choose a voter at random (all voters equally likely) from Minneapolis. Let A be the event that the

voter favors the mayor, and B be the event that the voter favors the police chief.

(b) Two people are selected at random from Minneapolis. Let A be the event that the first person favors

the mayor, while B is the event that the 2nd person favors 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 Minneapolis. 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."

Solutions

Expert Solution

(a) We choose a voter at random (all voters equally likely) from Minneapolis. 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 Minneapolis. 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.

- 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 Minneapolis. 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

milcah answered 1 year ago
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