First, some practice questions. The scenario below is relevant to questions #1-#3.

There are two sets of letters, and you are going to pick exactly one letter from each set.

Set #1 =

Set #2 =

**Q1**. What is the probability of picking a

A.

B.

C.

D.

E.

**Q2**. What is the probability of picking a

A.

B.

C.

D.

E.

**Q3**. What is the probability of picking two vowels?

A.

B.

C.

D.

E.

**Q4**. In a certain corporation, there are

A.

B.

C.

D.

E.

**Q5**. In a certain corporation, there are

A.

B.

C.

D.

E.

Here is the absolute bare minimum you need to know for probability calculations on the QUANT:

**"AND" means MULTIPLY**

**"OR" means ADD**

Is this the whole story? Well, not exactly. But if you can't remember or don't understand anything else about probability, at least know these two bare-bones rules, because just this will put ahead of so many people. Just this is enough to solve the problems #1 and #3, although these alone could lead to problems on the others. Before we qualify these simplistic rules, we need to discuss two distinctions.

Two events are disjoint if they are mutually exclusive. In other words, two events are disjoint if the probability of their simultaneous occurrence is zero, that is, it is absolutely impossible to have them both happen at the same time. For example, different faces of a single die are disjoint: under ordinary circumstances, if you roll one die once, you can't simultaneously get, say, both a

If events **disjoint**, then we can use the **simplified OR rule**:

That's the case in which the simplified rule, OR means ADD, works perfectly. If events **not disjoint**, then we have to use the **generalized OR rule**:

The reason for that final term: we need to subtract the overlap. The events in the region "

Two events are independent if whether one happens has absolutely no influence on whether the other happens. In other words, knowing about the outcome of one event gives absolutely no information about how the other event will turn out. For example, if I roll two ordinary dice, the outcome of each die is independent of the other die. If I tell you I rolled two dice, and the first die was a

We have to be careful. If I shuffle a deck of cards, draw one, replace it, re-shuffle, and draw another, then the two cards are independent. BUT, if I shuffle the deck, draw one card, and then without replacement draw a second card, then they are not independent. For example, if the first card is the

Also, notice that there are many human situations which would be independent in a perfect just ideal world, but regrettably are not independent in a real world full of inequities. In a perfect world, gender and corporate promotion would be independent, but in practice, they are not. In a perfect world, race and criminal conviction would be independent, but in practice, they are not.

If events **independent**, then we can use the **simplified AND rule**:

That's the case in which the simplified rule, AND means MULTIPLY, works perfectly. If events **not independent**, then things get complicated. Technically, the "generalized AND rule" formula would involve a concept known as "conditional probability", which would lead into realms of probability theory that are tested less frequently on the GMAT. See that other blog that discusses conditional probability if you want to understand this advanced topic in more detail.

Having read this post, take another look at those practice questions, and see if you understand them better, before simply reading the explanations below. Be patient with yourself as you work through probability: it takes time to internalize these distinctions, such as "disjoint" and "independent". There will be more information in the next post in this sequence.

**Answer = A**

**Q2**. Picking an

Fortunately, we know the first two, and we calculated the value of the third term already in #1.

**Answer = E**

**Q3**. On the first pick, two of the five letters are vowels —

**Answer = B**

**Q4**. Here we have an AND question, and the parameters — gender and advanced degree — are not independent. If I tell you the gender of a certain employee, then that gives me information about how likely it is that this employee has an advanced degree. One parameter gives information about the other, which means they are not independent. Therefore, we cannot use the simplified AND rule. Fortunately, it is relatively easy here to calculate everything directly.

There are

**Answer = B**

**Q5**. In this corporation, there are

**Answer = D**