Simple Probability

Simple Probability

Find the probability of pulling a yellow marble from a bag

with 3 yellow, 2 red, 2 green,

and 1 blue (I'm assuming) marble.

The probability (I'll just say 'P' for probability)

The probability of picking a yellow marble.

So this is sometimes the event in question right over here,

picking the yellow marble.

I'll even write down the word, 'picking'.

And when you say probability,

it's really just a way of measuring the likelihood

that something's going to happen.

And the way were going to think about it is,

how many of the outcomes from this trial,

from this picking a marble out of the bag,

how many meet our constraints, satisfy this event?

And how many possible outcomes are there?

So let me write the possible outcomes right over here,

so possible outcomes.

And you'll see it's actually a very straight forward idea.

But I'll just make sure we understand

all the words that people might say.

So the set of all the possible outcomes:

Well, there's three yellow marbles.

So I could pick that yellow marble,

that yellow marble or that yellow marble.

These are clearly all yellow.

There's two red marbles in the bag.

So I could pick that red marble, or that red marble.

There's two green marbles in the bag.

So I could pick that green marble, or that green marble.

And then there's one blue marble in the bag.

There's one blue marble.

So this is all the possible outcomes

and sometimes this is referred to

as the sample space.

sample...the set of all the possible outcomes,

fancy word for just a simple idea.

When I pick something out of the bag

and that picking out of the bag is called a trial.

There's eight possible things that I can do.

So when I think of the probability of picking a yellow marble,

I want to think about, well what are all the possibilities?

Well, there's eight possibilities for my trial.

So the number of possible outcomes,

you could view it as the size of the sample space,

number of possible outcomes.

And it's as simple as saying,

look I have eight marbles.

And you say how many of those marbles meet my constraint,

that satisfy this event here?

Well, there's three marbles that satisfy my event.

There's three outcomes that will allow this event to occur.

I guess this is one way to say it.

So there're three right over here.

So number that satisfy the event,

or the constraint right over here.

So very simple ideas, but many times the words

make them more complicated than they need to.

If I say what is the probability of picking a yellow marble,

well how many different types of marbles can I pick?

Well there's eight different marbles I could pick

And then how many are yellow?

Well, there's three of them that are actually yellow.