Galaxy clusters are known to be very bright in X-ray and contain a large number of X-ray point sources within the X-ray emission. However, due to the fluctuations of the X-ray emission, it is very difficult to detect faint X-ray sources and to extract accurately the photometric properties of the X-ray point sources in galaxy clusters. In addition, the most X-ray telescopes show spatially varying point spread function (PSF) and suffer from severe vignetting. The Chandra Archival Survey of Galaxy Clusters project is a wide-area ($sim40deg^2$) survey of serendipitous Chandra X-ray sources in galaxy cluster fields, containing ~58,000 X-ray point sources in ~800 Chandra ACIS observations of ~600 galaxy clusters. This project aim to investigate the density environmental effects on the physical properties of the X-ray point sources, comparing physical properties of the X-ray point sources in galaxy clusters to those in typical fields. To utilize the sensitivity and detection probability of the X-ray point sources in galaxy clusters, we perform extensive Monte-Carlo simulations. In this poster, we compare the detection probability of the X-ray point sources in galaxy clusters to that of typical fields, and discuss quantitatively the difference between them.