Abstract A variation of Rosenstock's trapping model in which N independent random walkers are all initially placed upon a site of a one-dimensional lattice in the presence of a one-sided random distribution (with probability c) of absorbing traps is investigated. The probability (survival probability) Φ N ( t) that no random walker is trapped by time t for N⪢1 is calculated by using the extended Rosenstock approximation. This requires the evaluation of the moments of the number S N ( t) of distinct sites visited in a given direction up to time t by N independent random walkers. The Rosenstock approximation improves when N increases, working well in the range Dt ln 2(1−c)⪡ ln N , D being the diffusion constant. The moments of the time (lifetime) before any trapping event occurs are calculated asymptotically, too. The agreement with numerical results is excellent.