Answer to Question #14942 in Statistics and Probability for Mohammad

Question

A sender transmits maximum of Ns different packets to N receivers. From these packets, any receiver needs M packets, which do not need to be same for different receivers. Packets are lost by i_th receiver with prob. Pe_i. Considering that each packet is sent in one time slot, whenever (say after k>=M time slots) all receivers get M packets, transmission stops. However if this does not happen after Ns-1 packets are sent, sending the last packet (Ns_th) will automatically stops the transmission. I should note that even if a receiver (say R1) get the first M packets successfully, but others don't, this receivers has to wait until other receivers also get M packets (e.g if this happens after k_th slot: then we say the transmission of R1 becomes successful after k slots). Otherwise, it is said to successful after Ns. Now I am interested in the prob of successful transmission for a receiver.
Hint: the prob. of successful transmission after k slots for M<=k<Ns-1 is similar for all receivers, but for k=Ns ??