Jacob K. answered • 12/14/21
M.Sc in Economics and Data Science
So, with probability questions like this, I find it helpful to write out with words what the data we're looking at actually means, and then we can start to figure out what they're really asking of us.
So, in total, there are 58 students. Now, let's start writing down some things we can observe about the table
-First, I see that 25/58 students are arts, meaning 33/58 are business
So, that gives us the total ratio of the student body. Let's try breaking down the data by the student type, meaning Arts and business
-Next, I see that out of the 25 art students, 10/25 got an A, 3/25 got a B, and 12/25 got a C
-Similarly, I see that 16/33 business students got an A, 15/33 got a B, and 2/33 got a C
Now, lets try breaking down the data by the grade recieved
26 Students got an A
-of these 26 As, 10 were given to art students, 16 to business students
18 students got a B
-of these 18 Bs, 3 were art students and 15 were business students
14 students got a C
-12 were art students, 2 were business students.
So now we have all sorts of percentages about who got what and what kind of student did what kind of way, etc. Let's look at what the question asked and see if we can figure out what they want us to look for.
The probability that the student selected at random was an Art major given that they got a B. So, this means that we're only looking at the students who got a B. If the student got a B, the probability that the student is an Art major is 3/18, as out of the 18 students who recieved a B, only 3 of them were art students. 3/18=0.16666666=0.17.
I know the answer is a bit long winded, but it was meant to help explain the whole table to you and to give you an idea about what all this data means and what kinds of questions you're able to answer with a table like this. Hopefully in that breakdown you're able to see everything you might have been stuck on and this answer is able to help you! Good luck!
