A university class has 27 students: 13 are business majors, 8 are art majors, and 6 are accounting majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a business major and the second student is an accounting major?Do not round your intermediate computations. Round your final answer to three decimal places.(If necessary, consult a list of formulas.)
Question
A university class has 27 students: 13 are business majors, 8 are art majors, and 6 are accounting majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a business major and the second student is an accounting major?Do not round your intermediate computations. Round your final answer to three decimal places.(If necessary, consult a list of formulas.)
Solution
To find the probability that the first student selected is a business major and the second student is an accounting major, we need to calculate the probability of these two events happening consecutively.
Step 1: Calculate the probability of selecting a business major as the first student. There are 13 business majors out of a total of 27 students. Therefore, the probability of selecting a business major as the first student is 13/27.
Step 2: Calculate the probability of selecting an accounting major as the second student, given that the first student selected was a business major. After selecting the first student, there are 26 students remaining, out of which 6 are accounting majors. Therefore, the probability of selecting an accounting major as the second student, given that the first student was a business major, is 6/26.
Step 3: Multiply the probabilities from Step 1 and Step 2 to find the overall probability. The probability of the first student being a business major and the second student being an accounting major is (13/27) * (6/26) = 78/702.
Step 4: Simplify the fraction and round the final answer to three decimal places. The simplified fraction is 13/117. Rounding this to three decimal places gives the final answer as 0.111.
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