# Important Formulas - Probability - Tricks & Shortcuts

**1. Experiment:**

An operation
which can produce some well-defined outcomes is called an

**experiment**.**2. Random Experiment:**

An
experiment in which all possible outcomes are know and the exact output cannot
be predicted in advance, is called

**a random experiment**.**Examples:**

i. Rolling
an unbiased

**dice**.
ii.Tossing a
fair

**coin**.
iii. Drawing
a card from a pack of well-shuffled

**cards**.
iv. Picking
up a ball of certain colour from a bag containing balls of different

**colours**.**Details:**

i. When we
throw a coin, then either a

**Head (H)**or a**Tail (T)**appears.
ii. A dice
is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we
throw a die, the outcome is the number that appears on its upper face.

iii. A pack
of cards has 52 cards.

It has 13
cards of each suit, name

**Spades, Clubs, Hearts and Diamonds**.
Cards of
spades and clubs are

**black cards**.
Cards of
hearts and diamonds are

**red cards**.
There are 4
honours of

**each unit.**
There are
Kings, Queens and Jacks. These are all called

**face cards**.**3.Sample Space:**

When we
perform an experiment, then the set S of all possible outcomes is called the

**sample space.****Examples:**

i.In tossing
a coin, S = {H, T}

ii. If two
coins are tossed, the S = {HH, HT, TH, TT}.

iii. In
rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.

4.

**Event:**
Any subset
of a sample space is called an

**event.****5. Probability of Occurrence of an Event:**

Let S be the
sample and let E be an event.

Then, E ⊆
S.

P(E) = n(E)/
n(S)

**6. Results on Probability:**

i. P(S) = 1

ii. 0 ≤ P
(E) ≤ 1

iii. P(Ï•)
= 0

iv. For any
events A and B we have : P(A ∪ B)
= P(A) + P(B) - P(A ∩ B)

v. If Ä€
denotes (not-A), then P(Ä€) = 1 - P(A).

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Important Formulas - Probability - Tricks & Shortcuts
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