Original subtitles

Instructor: Welcome back everybody.

So far we've only talked about events

and the theoretical probability

of which remains unaffected by other events.

We call these independent, and the simplest example

is flipping a coin.

You always have a 50% chance of getting tails

regardless of the result obtained with the previous throw.

In addition, we can have dependent events.

Their probabilities vary as conditions change.

For instance, take the probability

of drawing the queen of spades.

Normally the answer is 1 over 52

since we have exactly one favorable outcome

and 52 elements in the sample space.

Now, imagine we know that the card we drew was a spade.

Our chances of getting the queen of spades suddenly go up

since the new sample space contains

the 13 cards from the suit only.

Therefore, the probability becomes 1 over 13.

Okay, now imagine a different scenario.

Instead of a spade, we know our card is a queen

so the sample space only consists of four cards.

Therefore, the probability of drawing

the queen of spades becomes 1 over 4.

With this example, you could clearly see how the probability

of an event changes depending on the information we have.

This is a very important insight relating

to this whole section.

Okay, before we move on, let's introduce some new notation.

As usual, suppose we have two events, A and B,

to express the probability of getting A,

if we are given that B has occurred.

We use the following notation, P(A|B).

We read this as P of A given B.

Going back to our card example,

event A is drawing the queen of spades

and event B is drawing a spade.

Therefore, P of A given B would represent

the probability of drawing the queen of spades,

if we know the card is a spade.

We already calculated this earlier,

so P of A given B equals 1 over 13.

Similarly, if event C represents getting a queen

then P of A given C expresses the likelihood

of getting the queen of spades, assuming we drew a queen.

Thus, P of A given C equals 1 over 4.

Perfect, we call this probability

the conditional probability, and we use it

to distinguish dependent from independent events.

In the next lecture, we are going to show you

how to compute it and interpret conditional probabilities.

Thanks for watching.