All language subtitles for 02 - Calculate compound probabilities

- [Instructor] In the previous movie,

I described how to calculate simple probabilities,

that is the probability of a single trial.

In this movie, I will describe compound probabilities.

Compound probabilities assume that you

want to analyze multiple independent trials.

And by independent, that means that the second trial

or outcome, in other words, the second flip of a coin

or a throw of a die, is independent of the first.

If you do have multiple independent trials,

then you will multiply probability

to get a compound probability.

So flipping a coin will end up on heads half the time.

So the probability of getting heads twice in a row

assuming that the coin is fair

would be one half times one half equals one quarter.

One easy mistake to make is

to assume that compound probability

after you've already started.

In other words, one of the trials has been done.

If you're flipping a coin,

again, a fair coin,

with a one half probability of getting heads

and you flip and get heads,

the probability of flipping heads twice in a row

is no longer one quarter.

It is one half because you've already done it once.

And all that matters is the second trial

which is 50% or one half likely to end up on heads.

To visualize the probabilities,

I have created a chart.

And you can see that I have two separate trials in the rows.

In the first we have independent outcomes rolling a die.

And we're asking the probability

of rolling a three on the first outcome

and rolling a three again on the second one.

Assuming everything is independent,

then we have one chance out of six,

each of those trials to come up a three.

So that would be 1/6 times 1/6 equals 1/36.

So we have one chance out of 36

or 35 to one odds against.

We might also ask what is the probability

of rolling exactly a three on the first outcome

and not rolling a three,

in other words getting any other number

on the second outcome?

Well, for that, we have our probability of 1/6

of rolling a three,

and then we have five out of six numbers

that would allow us to succeed in our scenario.

So we multiply 1/6 by 5/6,

and get 5/36.

And those numbers make sense.

If we look back at the first row

and we see that we have 1/36 of rolling a three,

if we add that to 5/36 in the second row

where we don't roll a three,

we get 6/36, which is 1/6,

and is the probability of rolling a three

in the first place.

Compound probabilities can get a little tricky,

but after you make sure

that the results of your trials are independent

you can use multiplication to find

the compound probability of the composite outcome

you're looking for.