Step 1: Rank the groups by closeness of genes:
Identical twins share all their genes. Fraternal twins and ordinary siblings share about half. Unrelated people share almost none.
The correlation of intelligence should fall as the genetic link weakens.
Step 2: Place the known values on this ladder:
Identical twins together: about 0.86. Identical twins apart: about 0.72. Fraternal twins together: about 0.60. Siblings together: about 0.50. Unrelated children together: about 0.25.
Step 3: Pick the right rung:
The question talks about identical twins who live in different homes. Their genes are the same but their homes differ, so the value sits a little below the 0.86 of twins raised together. That value is 0.72.
Step 4: Reject 0.60:
This is the value of fraternal twins reared together, who share only half their genes. So it does not fit.
Step 5: Reject 0.50:
This is the value of siblings raised together. So it does not fit.
Step 6: Reject 0.25:
This is the value of unrelated children reared in the same home. It is far too low for identical twins. So it does not fit.
Step 7: Conclude:
Only 0.72 fits, so option 1 is correct.
Final Answer:
The value is 0.72.
\[ \boxed{0.72} \]