Question

Constructed Response 11

A random survey was conducted to gather information about age and employment status. This table shows the data that were collected.

What is the probability that a randomly selected person surveyed has a job, given that the person is less than 18 years old? Explain your answer and show your work!

Answer 1

What is the probability that a randomly selected person surveyed has a job, given that the person is less than 18 years old?

Solution: Let S be the Total number of people and S = 944

Let A be the number of people who have job and A = 607

`\therefore P(A) = (A)/(S) = (607)/(944)`

Let B be the number of people who are less than 18 years old and B = 265

`\therefore P(B) = (B)/(S) = (265)/(944)`

Also the number of people who have job and are less than 18 years old (A and B) = 20

`\therefore P(A and B) =  (A and B)/(S)=(20)/(944)`

We have to find the conditional probability of a person has a job given the person is less than 18 years old.

`P(A|B) = (P(A and B))/(P(B))`

`=((20)/(944) )/((265)/(944) )`

`=(20)/(944) * (944)/(265)`

`=(20)/(265)=0.0755`

Therefore, the probability that a randomly selected person surveyed has a job, given that the person is less than 18 years old is 0.0755