Answer:
0.6196
Step-by-step explanation:
The probability of an event [tex] A [/tex] given that event [tex] B [/tex] has occurred is denoted as [tex] P(A|B) [/tex] and is calculated using the formula:
[tex]\Large\boxed{\boxed{ P(A|B) = \dfrac{P(A \cap B)}{P(B)}}} [/tex]
In this case:
Event [tex] A [/tex] is being white.
Event [tex] B [/tex] is being 16- to 17-year-olds.
The probability that a randomly selected dropout is white and 16- to 17-year-olds is [tex] P(A \cap B) = 5.7\% [/tex].
The probability that a randomly selected dropout is 16- to 17-year-olds is [tex] P(B) = 9.2\% [/tex].
Now, substitute these values into the formula:
[tex]P(\textsf{white | 16-17 years old}) = \dfrac{P(\textsf{white and 16-17 years old})}{P(\textsf{16-17 years old})}\\\\= \dfrac{5.7\%}{9.2\%} \\\\ = \dfrac{ 5.7 \div 100}{ 9.7 \div 100 } \\\\ = \dfrac{0.057}{0.092} \\\\ = 0.619565217391 \\\\= 0.6196 \textsf{( in 4 decimal places)}[/tex]
Therefore, the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old, is 0.6196.
