We have two binary symmetric channels $1$ & $2.$

Channel $1$ has an error probability of $0\mathrm{.}12$ and channel $2$ has an error probability of $0\mathrm{.}23.$

a$)[4]$ If we want to transmit a bit sequence of ten bits, for each channel $($channel $1$

and channel $2),$ what is the probability $($with four decimal places$)$ that:

i$.$ A two$-$bit error occurs?

ii$.$ A three$-$bit error occurs?