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CAT exam is all about how smartly you solve the question in the quickest way. To help you with that, we at EduRev have started a summary sheet of formulae which will have all the shortcuts & formulae in one sheet. In this document you would be revising all the important parts of Probability, this document helps you in understanding the shortcuts & formulae of probability in a faster way.**Important Tips & Formulae of Probability**

The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes. The probability of an event A, symbolized by P(A), is a number between 0 and 1, inclusive, that measures the likelihood of an event in the following way:

- If P(A) > P(B) then event A is
**more likely**to occur than event B. - If P(A) = P(B) then events A and B are
**equally likel****y**to occur. - Two events are mutually exclusive if the intersection of two events is null (A ∩ B = φ)
- If E and F two events then P(E U F) = P(E) + P(F) - P(E and F together)
- If an event E is sure to occur, you say that the probability of event E is equal to 1 and you write P (E) = 1. Such events are known as
**certain events.** - If an event E is sure not to occur, you say that the probability of the Event E is equal to 0 and you write P(E) = 0. Such events are known as
**impossible events.** - The probability of E not occurring, denoted by P(not E), is given by P(not E) or P
- The odds in favor of occurrence of the event A are defined by m: n – m i.e., P (A): P () and the odds against the occurrence of A are defined by n – m : m, i.e., P (): P (A)
- To find the probability of two or more independent events occurring in sequence, find the probability of each event occurring separately, and then multiply the answers.

**Example: If a number is selected at random from the 2 digit 6 multiples, what is the probability that it is divisible by 9?****Solution.** Total 6 multiples = 12, - - - -, 96 ⇒ 15.

Required numbers are both multiples of 6 & 9

i. e, the multiples of 18. Those are 18, 36,- - - -, 90, total 5.

∴ Ans = **Practice Question **

Try yourself:Out of 13 applicants for a job, there are 5 women and 8 men. Two persons are to be selected for the job. The probability that at least one of the selected persons will be a woman is:

View Solution

=

∴ Ans =

i.e,

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