# Equally Likely Outcomes

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

A coin has got two sides, head and tail. If we toss a coin then there is an equal likelihood of getting a head or a tail. Hence, tossing a coin is an example of equally likely outcomes. For the experiment of 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

From a deck of $52$ cards, if we are choosing a card randomly then the probability of getting any card out of all $52$ cards is equally likely. Total size of sample space is, $n(S)$ = $52$.

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

Rolling a dice can have $6$ outcomes, $1, 2, 3, 4, 5, 6$ as each number is written on different sides of the cubic shaped dice. The likelihood of getting any number is equal as the all sides of a dice is equal in area. Hence, all sides are equally likely to come when a dice is rolled.
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

If a bag has n number of balls of same size then the likelihood of getting any ball when one ball is selected at random is equal. For example, if a bag has $5$ balls of same size then to get any ball, if a ball is selected at random, is same.

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.