A message consists of a string of bits $(0$s and $1$s$).$ Due to noise in the communications channel, each bit has probability $0\mathrm{.}3$ of being reversed $($i$.$e$.,$ a $1$ will be changed to a $0$ or a $0$ to a $1).$ To improve the accuracy of the communication, each bit is sent five times, so$,$ for example, $0$ is sent as $00000.$ The receiver assigns the value $0$ if three or more of the bits are decoded as $0,$ and $1$ if three or more of the bits are decoded as $1.$ Assume that errors occur independently.