Question

according to a recent study, 8.9% of high school dropouts are 16 - to 17 - year - olds. in addition, 6.1% 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: Recall the conditional probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that the dropout is white and \(B\) be the event that the dropout is 16 - 17 years old. Then \(P(A\cap B) = 6.1\%=0.061\) and \(P(B)=8.9\% = 0.089\).

Step2: Substitute the values into the formula

Substitute \(P(A\cap B) = 0.061\) and \(P(B)=0.089\) into \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). So \(P(A|B)=\frac{0.061}{0.089}\).

Step3: Calculate the value

\(\frac{0.061}{0.089}\approx0.6854\)

Answer:

\(0.6854\)