I have this exercise in the calculation of probabilities: In a binary communication channel, 40% of the time the value 1 is transmitted; the probability of correctly receiving a transmitted 0 value is 0.90 and the probability of correctly receiving the transmitted value 1 is 0.95. Decide (a) The probability of receiving the value 1.
(b) The probability that the value 1 was transmitted if that was the value received.
Being U = The communication channel transmits the value 1; C = The communication channel transmits the value 0; F = Probability of failure; From the statement I get
Pr (U) = 0.40
Pr (C) = 0.60
Pr ($F^\complement $ | U) = 0.90
Pr ($F^\complement $ | C) = 0.95
For a), the statement itself is giving it to me, although with the data I can also calculate it as
Pr (U and $F^\complement $) + Pr (U and F) = 0.40
For b) they ask me for a conditional Pr ($F^\complement $ | U) that they also give it to me as part of the statement.
I was surprised that this exercise is so easy, so I would like someone to confirm if it is good or badly done