# Constructed Response 11A 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!

Question

Answer:

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 = 944Let A be the number of people who have job and A = 607[tex]\therefore P(A) = \frac{A}{S} = \frac{607}{944}[/tex]Let B be the number of people who are less than 18 years old and B = 265[tex]\therefore P(B) = \frac{B}{S} = \frac{265}{944}[/tex]Also the number of people who have job and are less than 18 years old (A and B) = 20[tex]\therefore P(A and B) = \frac{A and B}{S}=\frac{20}{944}[/tex]We have to find the conditional probability of a person has a job given the person is less than 18 years old.[tex]P(A|B) = \frac{P(A and B)}{P(B)}[/tex] [tex]=\frac{\frac{20}{944} }{\frac{265}{944} }[/tex] [tex]=\frac{20}{944} \times \frac{944}{265}[/tex] [tex]=\frac{20}{265}=0.0755[/tex]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
solved

general
9 months ago
8471