Consider a binary channel with a cross over probability of $0\mathrm{.}15$ and an erasure probability of $0\mathrm{.}1,$ what is the capacity of the channel? In other words, when a bit is sent through the channel, there is a probability of $0\mathrm{.}15$ that the bit is flipped, a probability of $0\mathrm{.}1$ that the bit got erased $($the decoder can't even tell if the received bit is $0$ or $1),$ and a probability of $0\mathrm{.}75$ that the bit is transmitted correctly.