Example 1 Remove the big and small jokers from a deck of cards, and randomly draw five cards from the remaining 52 cards. The probability that at least two of the cards have the same number (or letter $K, Q, J, A$) is $\qquad$ (require calculating the numerical value of this probability, accurate to 0.01).
(2014, National High School Mathematics League (B Volume))
【Analysis】Let event $A$ be “drawing five cards randomly from 52 cards, where at least two cards have the same number (or letter $K, Q, J, A$)”. Then event $\bar{A}$ is “drawing five cards randomly from 52 cards, where each card has a different number (or letter $K, Q, J, A$)”.

The total number of cases is $\mathrm{C}_{52}^{5}$; the number of cases where event $\bar{A}$ occurs: choose five numbers (or letters) from 13 numbers (or letters), there are $\mathrm{C}_{13}^{5}$ ways to choose, and each number (or letter) has four suits, with a total of $4^{5}$ ways to choose, so the number of cases where event $\bar{A}$ occurs is $C_{13}^{5} \times 4^{5}$.
$$
\text { Thus, } P(\bar{A})=\frac{\mathrm{C}_{13}^{5} \times 4^{5}}{\mathrm{C}_{52}^{5}} \approx 0.5071 \text {. }
$$

Therefore, the probability of event $A$ occurring is approximately
$$
P(A)=1-P(\bar{A}) \approx 0.49 .
$$