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This table shows the majors of some 200 business students classified by gender.
I will be answering the following questions based on this table.
These questions can be answered intuitively, but I will also be using basic probability
rules to answer them.
First we find the row totals, and then the column totals.
#1: What is the probability of selecting a student majoring in Finance?
Here we see that there are 35 students in Finance out of the 200.
Therefore, the probability that a student majors in Finance is 35/200 which gives .175.
#2: What is the probability of selecting a Female Marketing student?
This is means that the student is Female and majors in Marketing?
From the table we can see here that there are 60 students who are female and also in
marketing.
Therefore, the probability is 60/200 which gives 0.3.
#3: What is the probability of selecting a student in Accounting or Finance?
Here we have 75 in Accounting and 35 in Finance.
The probability can be found by simply adding the two values and dividing by 200.
Or technically speaking, the two events (Accounting & Finance) are mutually exclusive.
That is, a student can major either in Accounting or in Finance but not both.
Therefore, the probability can be found by simply adding the probabilities of the 2 events.
So we have 75/200 plus 35/200 which gives 110 over 200 or 0.55.
#4: What is the probability of selecting a Male or a Finance student?
We can answer this by simply adding up all values in cells relating to males and to finance,
and dividing the result by 200.
We can also apply the addition rule.
That is, P(Male or Finance) equals
P(Male) + P(Finance) – P(Male & Finance)
which gives
85/200 + 35/200 – 25/200 and that equals 95/200 or 0.475
#5: What is the probability of selecting a Female, given she is in Accounting?
We write this as P(Female given Accounting).
The vertical line here represents the word “given”.
That is, out of the Accounting Students, what proportion is female?
Using conditional probability formula we write: P(Female and Accounting) divided by P(Accounting).
And this gives 45/75 or 0.6
#6: If a student is female, what is the probability that she is in Accounting?
The word “if” here plays the same role as the word “given” that we saw in the
last example.
In essence, we are looking for the probability of Accounting “given” Female.
That is, what proportion of the female students are in Accounting.
So we take the number of accounting students that are females, and divide by the number
of female students.
And that equals 45/115 which gives 0.391.
#7: If 2 students are selected, what is the probability that both of them major in Marketing?
We will assume the selections are made without replacement.
The probability that the first student is in Marketing is 90/200.
If the first selection is not replaced, then we have 89 marketing students, and 199 students
left in total.
So the probability of selecting a second marketing student given the first was also a marketing
student is 89/199.
Therefore, the probability that both are marketing student is
90/200 × 89/199 which is approximately 0.201.
And that concludes this video.
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