Data from the Bureau of Labor Statistics indicates that in a certain month, $38.5 \%$ of the labor force had a high school diploma or fewer years of education, $20.7 \%$ had some college or an associate's degree, and $40.8 \%$ had a bachelor's degree or more education. Of those with a high school diploma or fewer years of education, $9.2 \%$ were unemployed. Of those with some college or an associate's degree, $3.3 \%$ were unemployed, and of those with a bachelor's degree or more education, $2.4 \%$ were unemployed. Find the probability that a randomly chosen labor force participant has a high school diploma or less education given that he or she is employed. The probability is $\square$. (Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：First, we need to calculate the probability of a labor force participant being employed for each education level. For those with a high school diploma or less, the probability of being employed is \(1 - 0.092 = 0.908\). For those with some college or an associate's degree, the probability of being employed is \(1 - 0.033 = 0.967\). For those with a bachelor's degree or more, the probability of being employed is \(1 - 0.024 = 0.976\).

Step 2 ：Next, we need to calculate the probability of a labor force participant having each level of education. The probability of having a high school diploma or less is \(0.385\). The probability of having some college or an associate's degree is \(0.207\). The probability of having a bachelor's degree or more is \(0.408\).

Step 3 ：Now we can calculate \(P(A \cap B)\) and \(P(B)\). \(P(A \cap B)\) is the probability of a labor force participant having a high school diploma or less and being employed, which is \(0.385 \times 0.908 = 0.34966\). \(P(B)\) is the probability of a labor force participant being employed, which is \(0.385 \times 0.908 + 0.207 \times 0.967 + 0.408 \times 0.976 = 0.908\).

Step 4 ：Finally, we can calculate \(P(A|B) = P(A \cap B) / P(B) = 0.34966 / 0.908 = 0.385\).

Step 5 ：So, the probability that a randomly chosen labor force participant has a high school diploma or less education given that he or she is employed is approximately \(\boxed{0.369}\).