Consider n people P1,…,Pn. P1 receives binary information "yes" or "no" and will pass this information along to P2. More generally, Pi will pass information along to Pi+1. However, Pi will transfer the information that they hear with probability p and transfer the opposite information with probability 1−p, where 0<p<1, independent of all other people. Let Ai be the event that Pi transfers the original information (i.e. what P1 received) to Pi+1, and let the probability of this be pi. Compute n→∞limpn. If this limit does not exist, answer −1.
