### Online Exam » Aptitude » Probabilities

**Probabilities :**

**IMPORTANT FACTS AND FORMULAE**

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 known and the

exact output cannot be predicted in advance, is called a random experiment.

** Examples of Performing a Random Experiment: **

** **(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, namely 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 suit.

These are Aces, Kings, Queens and Jacks.

These are 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 of Sample Spaces :**

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

(ii) If two coins are tossed, then 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 space 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 (∅) = 0

(iv) For any events A and B, we have:

P (A∪B) = P (A) + P (B) – P (A∩ B)

v) If Â denotes (not-A), then PÂ = 1- P (A)