Question

according to a recent study, 9.2% of high school dropouts are 16 - to 17 - year - olds. in addition, 5.8% 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?
the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old, is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that a dropout is white and \(B\) be the event that a dropout is 16 - 17 years old.

Step2: Substitute the given values into the formula

We are given that \(P(B) = 0.092\) (probability of being 16 - 17 years old dropout) and \(P(A\cap B)=0.058\) (probability of being a white 16 - 17 years old dropout).

$$P(A|B)=\frac{0.058}{0.092}$$

Step3: Calculate the value

$$P(A|B)=\frac{0.058}{0.092}\approx0.6304$$

Answer:

\(0.6304\)