A message is being sent in binary code.

a$)[5$ pts$]$ Consider a message of length $1,$ i$.$e$.$ we send one bit, $0$ or $1.$ Let us assume that $0$ and $1$ are equally likely but that there is a $3\%$ chance of an error when we send $0$ but a $7\%$ chance of an error when we send $1.$ If the recipient gets a $1$ what is the probability that the original message was $1?$ Same for $0?$

b$)[10$ pts$]$ To reduce errors one can send each bit repeatedly. Assume that we send each bit $3$ times, so instead of a $0$ we send $000$ and instead of $1$ we send $111.$ The recipient interprets the message as whatever the majority of the bits was $($so e$.$g$.$ if you receive $101$ you assume that the message was $1).$ Assume the same error probabilities as in part a and that the bits are independent. If the recipient interprets the message to be a $1,$ i$.$e$.$ the majority of the $3$ received bits are $1,$ what is the probability that the original message was $1?$ What is the probability that the original message was $0$ if the majority of received bits are $0?$