I had to solve the following questions and I've provided all my work in order to get to the solutions. Could someone let me know whether I have done them properly?
Question(s):
There are 59 students, out of which 50 are writing the ela exam, 22 are writing a physics exam and 20 are writing both. Round answers to the nearest thousandth.
a) determine the probability, that a randomly selected student isn't writing the ela or physics exam.
b) determine the probability, that a randomly selected student is writing either the ela or the physics exam.
c) determine the probability, that a randomly selected student is writing only the physics exam.
established facts:
- 20 students are taking both exams (given)
- 30 (50 [ela students] - 20 [ela and physics students]) students are taking the ela exam
- 2 (22 [physics students] - 20 [ela and physics students]) students are taking the physics exam
- 7 (59 - [20 + 30 + 2]) students aren't taking either of the tests
visuals/different ways of viewing the problem?
let E represent the set of ela
let P represent the set of physics
let B represent the set of both ela and physics
E = {30}
P = {2}
B = {20}
or it can also be seen as:
My work:
a) take the # of students who aren't taking the exams (7) and divide it by the total # of students (59).
= 7/59 --> 0.119
b) using the non-mutually exclusive probability formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
where A is E (for ela) and B is P (for physics)
P(E∪P) = P(E) + P(P) - P(E∩P)
P(E∪P) = 50 + 22 - 20
P(E∪P) = 52
for the probability:
it's just taking P(E∪P) / 59 (total # of people)
= 0.881
c) we know that there are only 2 students writing just the physics exam.
all we have to do here is take the # of students taking just the physics exam and dividing it by the total # of students.
2/59 = 0.034