4. Consider the cards $A, 2, \cdots, J, Q, K$ as the numbers $1,2, \cdots, 11,12,13$. Now, place the 13 spades and 13 hearts together, and randomly draw 2 cards. The probability that the two cards have the same suit and their product is a perfect square is $\qquad$
There are $C_{26}^{2}$ ways to randomly draw 2 cards from 26 cards. The cases where the product of two numbers is a perfect square are 1,4; 1,9; 2,8; 3,12; 4,9, totaling 5 cases. Since there are two suits, the number of ways to draw 2 cards of the same suit and whose product is a perfect square is $C_{2}^{1} \cdot 5$.

Let $C=$ “randomly drawing 2 cards of the same suit and whose product is a perfect square,” so $P(C)=\frac{C_{2}^{1} \cdot 5}{C_{26}^{2}}=\frac{20}{26 \cdot 25}=\frac{2}{65}$.