00:01
In this problem, we have been given information about a random sample of students, and we need to find some probabilities.
00:08
So, first of all, considering the information given in the question, let us define a few events.
00:13
Let b be the event that a person is a business major.
00:16
Let e be the event that a person is an engineering major, and let o be the event that a person is some other major.
00:24
And let us consider f to be the event that a person is female.
00:27
Now, first of all, we have been asked to determine the probability that a person drawn at random is female.
00:33
Now, to determine this, we are going to use the law of total probability.
00:40
And to use the law of total probability, we need a set of mutually exclusive and exhaustive events.
00:46
We're going to use the events b, e, and o.
00:49
So using those three events and using the law of total probability, p of f is equal to p of b times p of f given b.
00:57
B plus p of e times p of f given e plus p of o times p of f given o times p of f given o so note that 50 % of the students indicated that they are business major so p of b is 50 % that's 50 over 100 or 0 .5 and out of the business major 60 % are female so p of f given b the probability of being female given that the person is a business major will be 60 % that's 0 .6.
01:28
So 40 % of the students are engineering majors, so p of e is 40 % or 0 .4...