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Probability is the most important and confusing topic on the quantitative section of standardized tests such as the GMAT and the GRE. Probability deals with the likelihood that some favorable outcome(s) will happen.

Probability is ratio of desired outcome(s) to the total possible outcomes.

Probability= Your desired outcome(s)/Total possible outcomes

**Example:**

What is the probability of having 6 while rolling a die?

There are total 6 possible outcomes and 1 outcome is 6.

Independent events: Two events are independent when the outcome of the first event does not influence the outcome of the second event.

When we determine the probability of two independent events we multiply the probability of the first event by the probability of the second event.

P(A and B)=P(A) – P(B)

Example:

What is the probability of having 6 and tail if you roll a die and toss a coin?

Probability of having tail = 1/2

Probability of having 6 = 1/6

P (tail and 6) = 1/2 x 1/6 = 1/12

Two events are mutually exclusive when two events cannot happen at the same time. The probability that one of the mutually exclusive events occur is the sum of their individual probabilities.

P (A or B) =P (A) +P (B)

Example:

In a jar there are 4 red, 3 blue and 3 white balls. If a ball is randomly picked what is the probability of having a red or a blue ball?

Probability of Red= 4/10

Probability of Blue= 3/10

P (Red or Blue) = 4/10 + 3/10 = 7/10

Inclusive events are events that can happen at the same time. To find the probability of an inclusive event we first add the probabilities of the individual events and then subtract the probability of the two events happening at the same time.

P (A or B) =P (A) +P (B)-P (A and B)

Example:

What is the probability of drawing a black card or a ten in a deck of cards?

There are 4 tens in a deck of cards P (10) = 4/52

There are 26 black cards P (black) = 26/52

There are 2 black tens P (black and 10) =

P (black or ten)= 4/52 + 26/52 – (2/52) = 7/13