I have a probability calculation which I hope someone can give advice on. I have a network with two routes in which I can send bits.
The first route consists of a single channel, with probability of transfer $p$. The first route can transfer a bit without any other requirements.
The second route consists of four channels, each with transfer probability $p$. They must all succeed for a bit to be transferred AND the channel from the first route must also succeed.
My first thought was that the number of bits, $n$ was simple given by
$$ n = p + p^5$$
however now I'm wondering I need to account for the dependence of the two channels on each other, but I'm not sure how to go about implementing this.
Thanks in advance to anyone who can help