Usually, you won’t be facing many probability questions in the GRE exam, and this is why many test aspirants start prioritizing questions that involve arithmetic algebra and geometry. But, if you’ve mastered the concepts of these topics, then turning your attention to probability can boost your performance on the D-day. Just like all the other concepts of GRE, the question of probability is also based on the basic concepts, the nuts, and bolts of probability that you studied in your grade school. However, to help you revise, we’ll guide you through the basic concepts of probability to master it on the D-day.

## Probability Formula

Probability asks you to find the likelihood of occurrence of an event. With this, it is easy to comprehend that the formula of probability is really straight forward. The range of an event happening always lies in between zero and one. This means that probability of an event can neither be negative nor more than one.

The probability of happening an event is denoted by P (E), whereas, the probability of not happening an event is denoted by P (E’).

\(Probability \; of \; the \; Occurrence \; of \; an \; event, P(E) = \frac{Number \; of \; Favourable \; outcomes (E)}{Total \; outcomes (S)}\)## Types of Events

Basically, there are two types of events:

- AND event: In this case unless and until all the conditions holds true, then only it will be added in the sets of events
- OR event: In this case if even a single condition holds true it will be included in the set of event, E

Let’s solve a problem to understand the working of this formula.

**Question**: A bag contains tickets numbered from 1 to 20. If a ticket is drawn at random from the bag then what is the probability that the ticket drawn from the bag has a number which is a multiple of 2 or 3?

\(A) \; \frac{1}{2}\)

\(B) \; \frac{13}{20}\)

\(C) \; \frac{2}{5}\)

\(D) \; \frac{7}{20}\)

**Solution**: In this question; Sample Space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Let event, E = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}

Therefore, \( Probability, P(E) = \frac{13}{20}\)

Let us solve another question but from the practice sets of GRE.

**Question**: A is chosen randomly from a set of {2, 5, 7, 16, 21}

B is chosen randomly from the set of {6, 11, 19, 22, 23, 27}

Calculate the probability that the sum of A and B will be 27.

**Solution:** Since, any of the first set can be combined with the second. Hence, total combinations \(= 5 \times 6 = 30\)

Out of these combinations, only \((5 + 22), \; (17 + 11), \; and \; (21 + 6)\) makes 27

\(So, \; P(E) \; = \frac{3}{30} = \frac{1}{10} = 0.1\)

**Read: **

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