0:03

The World Values Survey is an ongoing worldwide survey that polls the world

Â population about perceptions of life, work, family, politics, etc.

Â The most recent phase of the survey that polled 77,882 people from

Â 57 countries estimates that 36.2% of the world's population agree

Â with the statement, men should have more right to a job than women.

Â 0:29

The survey also estimates that 13.8% of people have a university degree or

Â higher and that 3.6% of people fit both criteria.

Â Let's start by listing what we know.

Â 36.2% of the world's population agree with the statement men should

Â have more right to a job than women.

Â So probability of agree is 0.362.

Â 13.8% of people have a university degree or higher, so

Â probability of a university degree is 0.138.

Â It's actually university degree or higher but

Â we'll just use a shorthand notation here.

Â And 3.6% of people fit both criteria.

Â So probability of agree and university degree is 0.036.

Â First question we'll tackle is are agreeing with the statement,

Â men should more right to a job than women, and

Â having a university degree or higher disjoint events?

Â Let's bring back the list of givens we listed earlier.

Â Since the probability of agreeing with this statement and

Â having a university degree or higher is not 0, the events are not disjoint.

Â Next we're asked to draw a Venn diagram summarizing the variables and

Â their associated probabilities.

Â We have two events that we determine to be non-disjoint, so we start by drawing

Â two overlapping circles, one for agree and one for university degree.

Â Then we mark the joint probability in the middle,

Â the 3.6% of people who fit both criteria.

Â 2:10

We know that the total percentage of those who agree is 36.2% and

Â this includes those who also have a university degree or higher.

Â So to find those who agree, but don't have a university degree,

Â we subtract the two probabilities and find that 32.6% of

Â people agree with the statement, but don't have a university degree.

Â Similarly, 13.8% of people have a university degree or

Â higher, and taking out those who also agree with the statement

Â leaves us with 10.2% of people who disagree with the statement but

Â have a university degree or higher.

Â Next we want to find the probability that a randomly drawn

Â person has a university degree or higher or

Â agrees with the statement about men having more right to a job than women.

Â Let's also put back on the screen what we know so far.

Â We're looking for the probability of agree or university degree.

Â And that should remind us the general addition rule, probability of A or B is

Â equal to probability of A plus probability of B minus probability of A and B.

Â Or, in context, probability of agree plus probability of university

Â degree minus probability of agree and university degree.

Â From here onwards, we can just plug in the probabilities that we already know.

Â That's 0.362 for P of agree, 0.138 for

Â P of university degree, and -0.036 for

Â the intersection, resulting in 0.464.

Â So there's about a 46% chance that a randomly drawn person has

Â a university degree or higher, or

Â agrees with the statement about men having more right to a job than women.

Â 4:08

An alternative way of getting at the same answer would be using the Venn diagram.

Â The desired probability is basically represented by the area covered by the two

Â circles.

Â So we could simply add all of the shown probabilities where we have already

Â adjusted for the double counting due to the joint

Â probability in the intersection of the two circles and arrive at the same answer.

Â 4:32

What percent of the world population do not have a university degree and

Â disagree with the statement about men having more right to a job than women?

Â We could simply phrase this as probability of neither agree nor

Â having a university degree, which is basically going to be the complement of

Â probability of agree or having a university degree that we found earlier.

Â We had found that that probability was 46.4%, so the complement is 53.6%.

Â On the Venn diagram, this is basically the area in the sample

Â space outside of agree and university degree.

Â Next we evaluate independence.

Â Does it appear that the event that someone agrees with the statement is independent

Â of the event that they have a university degree or higher?

Â Remember the product rule that says if A and B are independent,

Â probability of A and B is equal to probability of A times probability of B.

Â We can easily check if this is the case by setting up an equation where we check

Â if probability of agree and university degree equals probability

Â of agree times probability of university degree.

Â We have all three of these as givens from our introduction earlier, so

Â all we need to do is plug them in.

Â That is, is 0.036 equal to 0.362 times 0.138?

Â The right-hand side of the equation is approximately 5%, which is not equal

Â to 0.036, therefore we decide that the two events do not appear to be independent.

Â 6:22

Remember, probability of agree is 0.362 and

Â this is really the only relevant information for this question.

Â If selecting 5 people randomly, our sample space for

Â the number of people who might agree with this statement range from 0 to 5.

Â It is possible that none of them agree, just one agrees, two agree,

Â etc., all the way to all five agree.

Â 6:47

We're interested in instances where at least

Â one person agrees with this statement.

Â So we can divide up the sample space into two complimentary events, none indicated

Â by the 0 and at least 1 which covers all possible outcomes from 1 through 5.

Â To find the probability of at least 1 out of 5 people agreeing with the statement,

Â we simply subtract the probability of its complement, none agree, from 1.

Â So that is 1 minus the probability of all of them disagreeing.

Â Let's take a moment to think about this.

Â If none of them agree that basically means each one of them disagrees.

Â 7:29

So first we need to figure out what is the probability

Â that any given person disagrees with the statement?

Â That is also going to be a complement, and

Â it's the complement of the probability of agreeing, which we know to be 0.362.

Â So the probability that any given person disagrees with the statement is 0.638.

Â We're going to use this and we need five such people to make up our

Â desired outcome of five people all disagreeing with the statement.

Â 8:02

Plugging that back into the formula, we have 1 minus 0.638 to the 5th power.

Â We can multiply each one of these probabilities because we know that whether

Â one person in our group disagrees with the statement is independent of another

Â because we're randomly sampling them.

Â So the result comes out to be 0.894.

Â So there is roughly 89.4% chance that at least 1 person out of 5 randomly selected

Â people agree with the statement about men having more right to a job than women.

Â 8:39

In this example we brought together many of the concepts that we've learned

Â recently.

Â We touched on sample spaces, we talked about disjoint, complementary, and

Â independent events.

Â We also used the addition rule for unions of events,

Â as well as the multiplication rule for joint probabilities of independent events,

Â both to calculate further probabilities and to check independence as well.

Â