A class of 100 students contains four distinct groups. Group 1 contains 33 stude

Question

A class of 100 students contains four distinct groups. Group 1 contains 33 students with 15% marginal students. The second group of 25 students has 50% good. Two other groups contain 21 students each, with 20% and 15% marginal students respectively. We select at random one group of students and pick from it at random two students. a) What is the probability that these students are marginal? b) We examine the selected students as above and find them marginal. What is the probability that they were taken from group 1?

Explanation / Answer

a) P(2 students are marginal) = 1/4 * 30*0.15/30 * 29*0.15/29 + 1/4 * 25*0.50/25 * 24* 0.15/24 + 1/4 * 21*0.20/21 * 20*0.20/20 + 1/4 * 21*0.15/21 *20* 0.15/20 = 0.04

b)P(group1/marginal) = P(marginal/group1)*P(group1) / {P(marginal/group1)*P(group1) + P(marginal/group2)*P(group2)+P(marginal/group3)*P(group3) + P(marginal/group4)*P(group4)  }

= 0.15 * 0.15 * 1/4 / {0.015 * 0.015 * 1/4 + 0.50 * 0.50 * 1/4 + 0.20 * 0.20 * 1/4+0.15 * 0.15 * 1/4} = 0.071

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