6. Suppose that occupations are grouped by into three categories based on wages,

Question

6. Suppose that occupations are grouped by into three categories based on wages, Upper (U) Middle (M), and Lower (L). We are interested in "social mobility," which has to do with transitions between occupation groups between gencrations. We wil let Ui, Mi, and L denote the event that a father is in the Upper, Middle, or Lower occupation group, respectively, and U2, M2, and L2 denote the event that the son is in the Upper, Middle, or Lower occupation group. Glass and Hall (1954) compiled statistics on occupational mobility in England and Wales, given in the following table. U2 M2 12 U1 45 48 07 M1 05 .70 25 11.01 .50 .49 The table gives conditional probabilities: the upper left entry tells us that P(U2U) = 45, the botton left entry tells us that P(U2 L1) = .01, the bottorn right entry tells us that P(L2L1)- .49, and so on. Suppose that in the fathers' generation, 10% are in U, 40% are in M, and 50% are in L. Then what is the probability that a son in the next generation is in the Upper occupation group (i.e., what is P(14))?

Explanation / Answer

P(U2) = P(U1)* P(U2/U1) + P(M1)*P(U2/M1)+P(L1)*P(U2/L1) = 0.10 * 0.45 + 0.40*0.05 + 0.50*0.01 = 0.07

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