.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 3 17 16 36
Female 14 15 6 35
Total 17 32 22 71
If one student is chosen at random,
A. Find the probability that the student was male:
B. Find the probability that the student was male AND got a "C":
C. Find the probability that the student was male OR got a "C":
D. If one student is chosen at random, find the probability that the student was male GIVEN they got a C'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(A) The answer is obvious: take the total from the row "Male", which is 36,
and relate it to the global total, which is 71
P = .
(B) Take the number from the cell, which is intersection of the row "Male"
and the column "C". This number is 16. Relate it to the global total, which is 71
P = .
(C) Take total from the row "Male": it is 36.
Take a total from the column C: it is 22.
Add these two values and subtract the number in the intersection the row "Male"
and column "C", which is 16.
So, you calculate 36 + 22 - 16 = 42. <<<---=== We subtract 16 in order for do not count it twice.
This is the number of people in the category "male or got a C".
Finally, relate it to the global total 71
P = .
(D) This question is about the conditional probability.
Since the say "GIVEN they got a C", this means that in calculation this probability
we can reduce our scope to column C.
In this column, we take the number from row "Male": this number is 16.
Finally, we relate this number 16 to the total in column C, which is 22.
The sough probability is P = = .
Solved. All question are answered with explanations.