Question

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 1

Answer: $\dfrac{7}{12}$

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,

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}$

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

Hence, the required probability = $\dfrac{7}{12}$