Original subtitles

Instructor: Hello everyone,

in this video, we are going to introduce

a very useful concept in probability, the additive law.

Recall when we introduced the concept

of unions earlier in the course.

We said that the union of two events, A and B,

is equal to their sum minus their intersection.

The additive law states something very similar.

The probability of the union of two sets

is equal to the sum of the individual probabilities

of each event minus the probability of their intersection.

Let's go back to the survey from the last lecture.

The union of women and vegetarians equal the sum

of probabilities of being a woman and being a vegetarian

minus the probability of being a vegetarian woman.

Numerically, this equals 0.47 plus 0.44 minus 0.15, or 0.76.

Thus, if we picked a random person

from the survey there is a 76% chance

they're either female, vegetarian, or both.

Now, look at a different example.

Suppose we know 38% of our colleagues

can proficiently use Tableau and 45% are experts in SQL.

Additionally, 66% of the people

in the office are good with at least one of the two.

What is the probability of somebody being able

to simultaneously implement SQL and Tableau?

To answer this, we can rearrange

the additive law to get the intersection

of Tableau and SQL users equals the sum

of SQL and Tableau users minus their union.

Plugging in the values we are given results

in 38% plus 45% minus 66%, or 17%.

Transforming this into a probability gives us

a likelihood of 0.17 for somebody in the office

to be able to proficiently implement SQL and Tableau.

Certain events require the usage

of a new concept called the multiplication rule.

In the next lecture, we are going

to discuss when and how we apply it, thanks for watching.