I need help on doing some calculations regarding probability
Group A has 50 people, and group B has 300 people. All the members of both groups apply for the same selection process, and the selected people form a new group C
Out of group A’s 50 people, 20 people are chosen to group C. Out of group B’s 300 people, 60 people are chosen. That means 40% of group A was chosen and 20% of the people from group B were chosen.
Everyone were selected through the same selection process, so groups A and B were ”kind of” combined to a group AB, and from group AB a total amount of 80 (20+60) people were chosen to be a part of group C. We can clearly see, that if you were originally from group A, you were more likely to be selected for group C, but how do you calculate how much more probable it was for someone from original group A to be chosen over someone from original group B?
Other way to think about this: 50men and 300women apply for the same job(yes theyre looking for 80 employees in this case). 20 men were chosen and 60 women were chosen. How much more likely was it for a man to get the job, given that 40% of men were chosen and only 20% of women were chosen