Question

Let A denote the event that a person lives in New York City. Let P(A) = 0.5. Let B denote the event that the person does not live in New York City but works in the city. Let P(B) = 0.4. What is the probability that the person either lives in the city or does not live in the city but works there?
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Answer 1

The probability that the person either lives in the city or does not live in the city but works there is 0.9

Step-by-step explanation:

Given events

A: A person lives in a new York City

B: The person does not live in New York City but works in the city

Also,

$P(A)=0.5$

$P(B)=0.4$

Probability that the person either lives in the city or does not live but works there

$=P(A)+P(B)$

$=0.5+0.4$

$=0.9$

Hope this answer is helpful.

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Answer 2

Given : A denote the event that a person lives in New York City.  P(A) = 0.5 . B denote the event that the person does not live in New York City but works in the city.  P(B) = 0.4

To find : probability that the person either lives in the city or does not live in the city but works there

Solution:

A =   a person lives in New York City

P(A) = 0.5

B =  the person does not live in New York City but works in the city.

P(B) = 0.4

probability that the person either lives in the city or does not live in the city but works there = P(A U B)

P(A U B) = P(A) + P(B) - P(A∩B)

A∩B  = 0  here as Either person can live in city or can not live in city

P (A∩B ) = 0

=>  P(A U B) =  0.5  + 0.4 -  0

=> P(A U B) =  0.9

probability that the person either lives in the city or does not live in the city but works there = 0.9

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