Suppose a recent government report indicates that 12% of the labor force is African American. Of the individuals in the labor force who arc African American, 11% are unemployed. Among the individuals in the labor force who arc not African American. 5% are unemployed. Let A be the event that a randomly selected member of the labor force is African American and let B be the event that a randomly selected member of the labor force is unemployed. Determine P (A | B), the probability that a randomly selected member of the labor force is African American given that he or she is unemployed. Express your answer as a percentage with no decimal places.

P(A|B) = 0.231 = 23%

Step-by-step explanation:

A is the event that a randomly selected member of the Labor force is African American, P(A) = 0.12 (given in the question)

Non African-Americans in the labour force, P(A') = 1 - P(A') = 1 - 0.12 = 0.88

B is the event that a member of the labor force is unemployed, P(B) is not directly given, but can be calculated from the given percentages on the question.

Total unemployed people in the labour force = unemployed African American people in the labor force + unemployed people in the labor force that aren't African Americans

African-Americans in the labour force P(A) = 0.12

Non African-Americans in the labour force, P(A') = 0.88

unemployed African Americans in the labor force P(A n B) = 0.11 of the African Americans in the labor force = 0.12 × 0.11 = 0.0132

Unemployed Non-African Americans in the labor force, P(A' n B) = 5% of 0.88 = 0.88 × 0.05 = 0.044

Total unemployed Americans in the labor force, P(B) = P(A n B) + P(A' n B) = 0.0132 + 0.044 = 0.0572

Probability that a person is African American, given that they're unemployed, P(A|B) = (P(A n B))/P(B) = 0.0132/0.0572 = 0.231 = 23%

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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