# Probability

Probability is the likelihood or chance of an event occurring.

Some Concepts

1. When we toss a coin, then either a Head (H) or a Tail (T) appears.
2. 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.
3. 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 four honours of each suit. These are Aces, Kings, Queens and Jacks. These are called Face cards.

The probability of a certain event occurring can be represented by P(A). The probability of a different event occurring can be written as P(B). Therefore, for two events A and B,

P(A) + P(B) - P(A ∩ B) = P(A ∪ B)

### Mutually Exclusive Events

Events A and B are mutually exclusive if they have no events in common. If two events are mutually exclusive,

P(A) + P(B) = P(A ∪ B)

### Independent Events

Two events are independent if (and only if)

(A ∩ B) = P(A)P(B)

### Conditional Probability

Conditional probability is the probability of an event occurring, given that another event has occurred.

P(A|B) means the probability of A occurring, given that B has occurred.

For two events A and B,

P(A ∩ B) = P(A|B)P(B)

P(A ∩ B) = P(B|A)P(A)