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The city council conducts a survey of the city's residents to determine which services are most used by the community. 60% of the residents say that they use the library, and 35% of the residents say they use the library and the recycling center. What is the probability that a resident uses the recycling center given that they use the library? Express your answer as a fraction in simplest form.

Answer :

JeanaShupp

Answer: [tex]\dfrac{7}{12}[/tex]

Step-by-step explanation:

Let A denotes the event of residents say that they use the library.

B denotes the event that residents say that they uses the recycling center.

As per given , we have

P(A)=0.60

P(A∩B)=0.35

Using conditional probability formula we have,

[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]

i.e. The probability that a resident uses the recycling center given that they use the library [tex]=\dfrac{0.35}{0.60}=\dfrac{35}{60}=\dfrac{7}{12}[/tex]

Hence, the required probability = [tex]\dfrac{7}{12}[/tex]

MrRoyal

The probability that a resident uses the recycling center given that they use the library is 7/12

Let A represent the event that the resident uses the library, and B represent the event that the resident uses the recycling center.

The given  parameters are:

[tex]\mathbf{P(A) = 60\%}[/tex]

[tex]\mathbf{P(A\ n\ B) = 35\%}[/tex]

The probability that a resident uses the recycling center given that they use the library is calculated as:

[tex]\mathbf{Pr = \frac{P(A\ n\ B)}{P(A)}}[/tex]

So, we have:

[tex]\mathbf{Pr = \frac{35\%)}{60\%}}[/tex]

Simplify

[tex]\mathbf{Pr = \frac{35}{60}}[/tex]

[tex]\mathbf{Pr = \frac{7}{12}}[/tex]

Hence, the required probability is 7/12

Read more about probabilities at:

https://brainly.com/question/11234923

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