The table below shows the probability that a mother in a given part of the income distribution (given by the row) will have a daughter in a given part of the income distribution (given by the column). So,for example, the daughter of a women with the income in the bottom third of the income distribution will herself have a 60% chance of being in the bottom third, a 25% chance of being in the middle third, and a 15% chance of being in the top third.

Income Group of Daughter

Income Group of Mother Bottom third Middle third Top third

Bottom third 0.6 0.25 0.15

Middle third 0.25 0.5 0.25

Top third 0.15 0.25 0.6

What is the probability that the granddaughter (along the maternal line) of a woman in the middle third ofthe income distribution will herself be in the middle third of the income distribution? (Hint: note that a woman in the second generation does not necessarily have to be in the middle third of the income distribution, so you need to take into account 3 cases: when the mother of the granddaughter is the top, in the middle, and in the bottom thirds of the income distribution.)