$3\mathrm{.}12$ Noisy reading from flash storage

Flash memories are a type of storage media which provide orders of mag$-$

nitude faster access to data as compared to hard disks. However, one of the

downsides of flash memories is that they are prone to error when reading.

You have two flash memory devices, F$1$ and F$2.$ The noisy readings from

F$1$ and F$2$ are modeled as follows:

F$1$: For any stored bit, the value read is flipped with probability $p_1.$

F$2$: For any stored bit, the value read is flipped with probability $p_2.$

Suppose you write a bit into both F$1$ and F$2($i$.$e$.,$ the same bit is written

into both devices$),$ and that F$1$ and F$2$ act independently on that bit. A day