A space probe communicates with NASA using bit strings. Suppose that for each bit it sends, the probability that it is a 1 is 0.3, so the probability that it is a 0 is 0.7. Now an issue with these kinds of communication is that occasionally the bits flip. Suppose NASA has observed that the probability a bit flips is 0.1. This means that the probability that NASA receives a 1 given that the space probe sent a 0 is 0.1; similarly, the probability that NASA receives a 0 given that the space probe sent a 1 is 0.1. Let SO and S1 denote the events that the space probe sent a 0 and a 1 respectively. On the other hand, let RO and R1 be the events that NASA received a 0 and a 1 respectively.

a. Write the values of Prob(S1), Prob(SO), Prob(R1/SO), Prob(RO/S1) from the problem statement.
b. What is Prob(S1n RO)? (i. e., the probability the space probe sent a 1 and NASA received a 0)
c. What is Prob(SO n RO)?
d. What is Prob(RO)?
e. Finally, what is Prob(SORO)?