According to a recent study, 9.3% of high school dropouts are 16- to 17-year-olds. In addition, 6.3% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?
Accepted Solution
A:
Answer: [tex]\dfrac{21}{31}[/tex]Step-by-step explanation:Let A represents the event that high school dropouts are 16- to 17-year-olds and B be the event that high school dropouts are white. Given : The probability of high school dropouts are 16- to 17-year-olds :[tex]P(A)=0.093[/tex]The probability of of high school dropouts are white 16- to 17-year-olds : [tex]P(A\cap B)=0.063[/tex]Then , the conditional probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old is given by :-[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.063}{0.093}=\dfrac{21}{31}[/tex]