Question

A survey was given to adult residents in a particular city. It found that 22% of the residents regularly use public transportation, and 85% of the residents have the ability to drive. 14% of the residents regularly use public transportation AND have the ability to drive. Find the probability that an adult resident in this city regularly uses public transportation, given that he or she has the ability to drive. Round to the nearest hundredth.

Answer 1

The probability that an adult resident in this city regularly uses public transportation, given that he or she has the ability to drive will be 93%.

What is the addition rule of size for two subsets?

For two subsets A and B of the universal set U, we have:

$\rm n(A \cup B) = n(A) + n(B) - n(A \cap B)$

A survey was given to adult residents in a particular city.

It found that 22% of the residents regularly use public transportation, and 85% of the residents have the ability to drive.

14% of the residents regularly use public transportation AND have the ability to drive.

Let P(A) be the probability of the adults that uses public transportation regularly and P(B) be the probability of the adults that has the ability to derive.

Then the probability that an adult resident in this city regularly uses public transportation, given that he or she has the ability to drive will be

n(A) = 0.22

n(B) = 0.80

n(A∪B) = 0.14

Then we have

$n(A \cap B) = 0.22 + 0.85 - 0.14\\\\n(A \cap B) = 0.93\\\\n(A \cap B) = 93\%$

Learn more about the addition rule for two subsets here:

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