# PRE-CLASS ASSIGNMENT – CONDITIONAL PROBABILITY

## PRE-CLASS ASSIGNMENT – CONDITIONAL PROBABILITY

You have a jar filled with 3 red marbles, 5 blue marbles and 2 black marbles. Our plan is to pick 2 marbles from the jar __without replacing the first one__.

1) Let’s say we want to find the probability you pick a blue marble second, given that you first pick a black marble. What is the original sample space, n(S), of the problem?

Once you remove a black marble from the jar, what is the new n(S)?

If you then want to pick a blue marble, how many blue marbles are left in the jar to choose from?

What is P(blue marble picked second given that a black marble was picked first)?

2) Now let’s say we want to find the probability you pick a blue marble second, given that you first pick a blue marble first. Once you remove the first blue marble, what is the new n(S)?

If you then want to pick your second blue marble, how many blue marbles are left in the jar to choose from?

What is P(blue marble picked second given that a blue marble was picked first)?

How does the first problem differ from the second one?

3) Find: P(black marble picked second given that a blue marble was picked first)

4) Find: P(black marble picked second given that a black marble is picked first)

When we want to know the probability that A occurs, given that we know B has already occurred, we write P(B|A). This is known as **conditional probability**. The words ‘given that’ are always an indication that we are looking at a conditional probability problem.