The armed force consists of 1200 officers, 960 men and 240 women. Over the past two years 324 officers have received promotions of which 288 are males' officers and 36 are female officers. This has raised an issue of gender bias especially from the general public. However, the defense minister has argued that the relative low numbers of promotions for female officers was not discrimination, but due to the fact that relative few females are members of the force. (1) Develop a joint probability table for the information above (2) Using the marginal probabilities, comment on the discrimination charge labeled against the force. (3) If an officer is selected at random, what is the probability that the officer is promoted given that she is a female? (4) If an officer is selected at random, what is the probability that the officer is promoted given he is a male? (5) Let A denote the event that an officer is female and B denote the event that the officer is not promoted. Are events A and B independent? Justify your