For a certain population of employees, the percentage passing or failing a job c
ID: 2956396 • Letter: F
Question
For a certain population of employees, the percentage passing or failing a job competency exam, listed according to sex, were as shown in the accompanying table. That is, of all the people taking the exam, 24% were in the male-pass category, 16% were in the male-fail category, and so forth. An employee is to be selected randomly from this population. Let A be the event that the employee scores a passing grade on the exam and let M be the event that a male is selected.Sex
| Outcome | Male (M) | Female (F) | Total |
Pass (A) 24 36 60
Fail (A bar) 16 24 40
Total 40 60 100 a Are the events A and M independent? b Are the events A bar and F independent? Can you please explain your reasoning I am really confused on figuring out when it's independent or not. Thank you. Total 40 60 100 a Are the events A and M independent? b Are the events A bar and F independent? Can you please explain your reasoning I am really confused on figuring out when it's independent or not. Thank you.
Explanation / Answer
To approach this, you need to consider what it means for 2 events to be independent or dependent. For example: If I ask what are the chances of rolling a die and getting an even number and flipping a coin and getting heads, this is independent. No matter what i roll on the die, it should have absolutely NO effect on the fact I want to flip a heads on a coin. A dependent event is just the opposite, that if I desire one outcome, it can directly influence the other outcome. So: Does the event of a passing score influence whether you will pick a male or female: No, so yes these should be independent Same with question b. Picking a failing score does not mean you will influence picking a male or female either. So in case a) and b) both should be independent! To give you an example of this being dependent. Lets say now that 0 males pass the test and only females pass the test. At this point is you say, I want a passing score, that will force you to pick a female, this would be dependent. Hope this helps!