A simple binary communication channel carries messages by using two signals 0 and 1.It was assumed that for a given binary channel, 40% of the time a lis transmitted; the probability that a transmitted 0 is correctly received is 0.90; the probability that lis correctly received 0.95. This information is illustrated in Figure 1 where A = event that 1 is transmitted. = event that 0 is transmitted. B = event that 1 is received. = eve t that 0 is received. A B Figure 1: A single- stage binary communication channel Determine P(B) and P(B) а. b. P(A/B) c. The stochastic matrix of the communication channel. d. If P(B/Ā) = P(C/B) and P(B/A) = P(C/B),find 3D i. P(C/B) ii. P(T/B) e. Figure 2 below illustrate information on a two- stage binary communication channel. Copy and complete the channel with the necessary probabilities.

Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?)P⁡(A) ?(?)P⁡(B) ?(?)P⁡(C) 0.6 0.4 0.9 What is the probability that the employee is not late for work?   (Round to 3 decimal places)

Jay-Z has applied to both The School of Hard Knocks and The University of OG's. He thinks the probability that The School of Hard Knocks will admit him is 0.4, the probability that The University of OG's will admit him is 0.5, and the probability that both will admit him is 0.2. Creating a Venn Diagram is Helpful. What is the probability that Jay-Z gets into The School of Hard Knocks but not The University of OGʻs?

Q. 2 Suppose the following three boxes are given: Box A contains 3 red and 5 white mobile phones Box B contains red and 1 white mobile phones Box C contains 2 red and 3 white mobile phones A box is selected at random, and a mobile phone is randomly drawn from the box. If the mobile phone is red, find the probability that it came from the box A.