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Question 6, 5.4.15
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According to a recent study, $9.3 \%$ of high school dropouts are 16 - to 17 -year-olds. In addition, $5.7 \%$ 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 $\square$.
(Round to four decimal places as needed.)

Step 1 ：According to a recent study, 9.3% of high school dropouts are 16 - to 17 -year-olds. In addition, 5.7% of high school dropouts are white 16- to 17-year-olds. We are asked to find the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old.

Step 2 ：This is a conditional probability problem. The probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old, is the probability of both events happening divided by the probability of the given event.

Step 3 ：In this case, the probability of both events happening is the probability that a dropout is a white 16- to 17-year-old, which is 5.7% or 0.057 in decimal form.

Step 4 ：The given event is that the dropout is 16 to 17 years old, which has a probability of 9.3% or 0.093 in decimal form.

Step 5 ：So, we need to divide the probability that a dropout is a white 16- to 17-year-old by the probability that a dropout is 16 to 17 years old. This gives us \( \frac{0.057}{0.093} = 0.6129032258064515 \).

Step 6 ：Rounding to four decimal places as needed, we get 0.6129.

Step 7 ：Final Answer: The probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old, is \( \boxed{0.6129} \).