Mark is appointed by brain technology. He is told that he should take a proficiency exam test after his first year and that 65% of all new hires pass the test. Furthermore he is told that 45.5% of new appoints pass the test and are promoted. Entire 70% of new hires are promoted. Suppose that these percentages can be interpreted as the probablity of events.
A) Draw joint probability table with passing the test upon the vertical axis and being promoted on the horizontal axis.
B) What is the probability that new hire fails the test?
C) Determine the probability that a new appoint is promoted given she passes the test.
D) The gossip around the water cooler is which promotions are based upon personality and who the boss likes the most, and passing test has nothing to do with getting promoted. You decide to employ the rules of probability to see if there is any validity to the rumor. Does passing the test affect the probability of getting promoted or are the two events independent? Explain