# Statistical Question (I believe...)

• Feb 19th 2010, 02:04 PM
AnAmericanInNederlands25
Statistical Question (I believe...)
The following problem has become a mind block and any help would be appreciated:

Of a group of one thousand students who did the examination for Mathematics as well as the examination for Statistics, it is known that 600 of them passed the Mathematics exam and 650 passed the Statistics exam. Moreover, 400 students passed both exams.

(a) How many students failed both exams?

(b) How many students passed one and failed the other exam?

I am not sure if this falls into probability or statistics. I am trying to figure out a formula by which to solve the equation.

Thanks for any help,

Matty
• Feb 19th 2010, 02:31 PM
vince
Quote:

Originally Posted by AnAmericanInNederlands25
The following problem has become a mind block and any help would be appreciated:

Of a group of one thousand students who did the examination for Mathematics as well as the examination for Statistics, it is known that 600 of them passed the Mathematics exam and 650 passed the Statistics exam. Moreover, 400 students passed both exams.

(a) How many students failed both exams?

(b) How many students passed one and failed the other exam?

I am not sure if this falls into probability or statistics. I am trying to figure out a formula by which to solve the equation.

Thanks for any help,

Matty

Ok, first reduce the space by 400 for the questions that follow, since effectively only 600 students are left of interest to us (1000-400=600).

a) Well of those 600, we know 200 passed the M-exam (600-400=200), and 250 passed the S-exam(650-400=250).Since none of these students passed both exams, we've already subtracted those, this means 600-(200+250) = 150 failed both exams.
b) Well this one is simple now, because
1000 = 400(passed both exams) + 150(passed neither exam) + x(passed one of the two exams). Solving for x, x=450.