of education, 25.7% had some college or an associate's degree, and 40.6% had a bachelor's degree or more education. Of those with a highployed, and of those with a bachelor's degree or more education, 3.5% were unemployed. Find the probability that a randomly chosen labor force Date from the Bureau of Labor Statistics indicates that in a certain month, 33.7% of the labor force had a high school diploma or fewer years of ed-school diploma or fewer years of education, 5.5% were unemployed. Of those with some college or an associate's degree, 3.9% were unemployparticipant has a high school diploma or less education given that he or she is employed.The probability is.(Type an integer or decimal rounded to three decimal places as needed.)

Conditional Probability: Let A and B be two events with P(A) > 0. Then the conditional probability of B given A, denoted by P(B | A), is defined as the probability of occurrent of the event B when it is assumed that the event A has already been occurred. It is given by the formula, Bayes' Theorem: Let A1, A2, ... , An be n mutually exclusive and exhaustive events with P(Ai) > 0 for all i = 1, 2, ... , n. Let B be another event with P(B) > 0. Then by Bayes' Theorem we have,Let A1 be the event that the randomly chosen labor force participant has a high school diploma or fewer years of education A2 be the event that the randomly chosen labor force participant has some college or an associate's degree A3 be the event that the randomly chosen labor force participant has a bachelor's degree or more education B be the event that the randomly chosen labor force participant is employed Clearly, A1, A2 and A3 are mutually exclusive and exhaustive. Then, Bc is the event that randomly chosen labor force participant is unemployed B | A1 is the event that the randomly chosen labor force participant is employed given he or she has a high school diploma or fewer years of education B | A2 is the event that the randomly chosen labor force participant is employed given he or she has some college or an associate's degree B | A3 is the event that the randomly chosen labor force participant is employed given he or she has a bachelor's degree or more education We are given, P(A1)=33.7%=0.337, P(A2)=25.7%=0.257, P(A3)=40.6%=0.406 and P(Bc|A1)=5.5%=0.055⇒P(B|A1)=1-0.055=0.945 P(Bc|A2)=3.9%=0.039⇒P(B|A2)=1-0.039=0.961 P(Bc|A3)=3.5%=0.035⇒P(B|A3)=1-0.035=0.965 Therefore, by applying Bayes' theorem, the probability that the randomly chosen labor force participant has a high school diploma or less education given that given that he or she is employed is Answer: The blank will be filled up with 0.333.