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Modern Maths

Probability

ALL MODULES

CAT 2025 Lesson : Probability - Concepts & Cheatsheet

Note: The video for this module contains a summary of all the concepts covered in this lesson. The video would serve as a good revision. Please watch this video in intervals of a few weeks so that you do not forget the concepts. Below is a cheatsheet that includes all the formulae but not necessarily the concepts covered in the video.

9. Cheatsheet

1

) P(E) =

\dfrac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}}

\dfrac{n\text{(E)}}{n\text{(S)}}

2

) Basic Properties
(a)

0 \leq

P(E)

\leq 1

(b) P

(\overline{\text{E}})

= 1 -

P(E)
(c) P(A

\cup

=

P(A)

+

P(B)

-

P(A

\cap

3

) Mutually exclusive events are those where only one of them can occur at a time, i.e., P(A

\cap

= \bm{0}

4

) Non-mutually exclusive events are those where more than

1

event can occur at a time, i.e. P(A

\cap

\ne

\bm{0}

5

) Probability of occurrence of two independent events (A and B) is P(A and B) = P(A)

\times

P(B)
Probability of both A and B not occurring is P(

\overline{\text{A}}

and

\overline{\text{B}}

)

=

(

1 -

P(A))

\times

(

1 -

P(B))

6

) Independent Events with

\bm{2}

outcomes: P(A occurring r times out of a total

n

)

=

^{n}C_{r}

[P(A)]

^{r}

[P(B)]

^{n - r}

7

) Dependent Events: P(A and B and C and ...)

=

P(A)

\times

P(B given A)

\times

P(C given A and B)

\times

...

8

) P(A / B) is the Conditional Probability of an event A occurring given that an event B has already occurred.

P(A / B)

= \dfrac{\text{P}(\text{A} \cap \text{B})}{\text{P}(\text{B})} =

\dfrac{n (\text{A} \cap \text{B})}{n(\text{B})}

9

) Odds for an event is the ratio of favourable to unfavourable cases.

Odds against an event is the ratio of unfavourable to favourable cases.

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