Solution:

Using Markov chains, grandson is son of a son

\(p_{ij}^{(2)} = \sum_{k=1}^{r} p_{ik}p_{kj}\)

4.

Here is \(i = H\) and \(j = H\), means \(H -> H ->H\) or \(H -> Y ->H\) or \(H -> D ->H\)

Expanding Morkov chains formula

\(p_{HH}^{(2)} = p_{HH}.p_{HH} + p_{HY}.p_{YH} + p_{HD}.p_{DH}\)

Substituting the values

\(p_{HH}^{(2)} = 0.8*0.8 + 0.2*0.3 + 0*.2 = 0.7\)

Probability that the grandson of a man from Harvard went to Harvard = \(0.7\). It means that there is \(70 \%\) chance that grandson of a man from Harvard went to Harvard.

5.

Using the same logic from above,

\(p_{HH}^{(2)} = 1*1 + 0*0.3 + 0*.2 = 1\)

Probability that the grandson of a man from Harvard went to Harvard = \(1\). It means that there is \(100 \%\) chance that grandson of a man from Harvard went to Harvard.