Problem #PRU-66041

Problem

When one scientist comes up with an ingenious idea, he writes it down on a piece of paper, but then he realises that the idea is not brilliant, scrunches up this sheet of paper and throws it under the table, where there are two rubbish bins. The scientist misses the first bin with a probability $p>0.5$, and with the same probability he misses the second. In the morning, the scientist threw five crumpled brilliant ideas under the table. Find the probability that there was at least one of these ideas in each bin.