Equally likely outcomes are of those events in a sample space who have same chance or same likelihood of occurrence. When all events of a sample space are having same chances of their occurrence then they are being called equally likely events. Events such as rolling a die, tossing a coin, choosing a card from a deck of cards or choosing a ball from a bag are all equally likely outcomes.

## Definition

Those events who have equal likelihood of their occurrence are known as equally likely outcomes. There are events such as rolling a die where all sides are equal and hence, the likelihood of getting any side is equal to the likelihood of getting any other side. But if there is a cubical shaped toy and we throw it then the likelihood of getting each side is not same as all sides differ in area.

## Tossing a Coin

Sample space,

**S = {H, T}**

Probability of getting a head, $P(A)$ = $\frac{1}{2}$

Probability of getting a head, $P(B)$ = $\frac{1}{2}$

## Choosing a Card from Deck of Cards

Getting a single card, number of favorable event $n(E)$ = $1$

Probability of getting any card, $P(E)$ = $\frac{1}{52}$

Choosing card randomly from deck of card will have equally likely outcome for any card.

## Rolling a Dice

Sample space, $S$ = $\{1, 2, 3, 4, 5, 6\}$

Total element in sample space, $n(S)$ = $6$

The probability of getting any number, that is, $1, 2, 3, 4, 5,$ or $6$ = $\frac{1}{6}$

## Drawing Balls from a Bag

Total number of elements in sample space, $n(S)$ = $5$

Probability of getting any ball = $\frac{1}{5}$

But if the bag is having $3$ red and $2$ white balls, then the probability of getting a red ball and a white ball is not equal. So, these events are not equally likely outcomes.