Probability is based on observations of certain events. Probability of an event is the ratio of the number of observations of the event to the total numbers of the observations. An experiment is a situation involving chance or probability that leads to results called outcomes. An outcome is the result of a single trial of an experiment. The probability of an event is the measure of the chance that the event will occur as a result of an experiment.

Probability of an event A is symbolized by P(A). Probability of an event A is lies between 0 ≤ P(A) ≤ 1.

Probability of an event A is symbolized by P(A). Probability of an event A is lies between 0 ≤ P(A) ≤ 1.

## Probability Formula

Probability Formula

Probability Formula

Probability of an Event = $\frac{Number\ of Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}$

Measures the likelihood of an event in the following way:

- If P(A) > P(B) then event A is more likely to occur than event B.

- If P(A) = P(B) then events A and B are equally likely to occur.

## What is the Formula for Probability

**The probability of an event tells that how likely the event will happen.**Situations in which each outcome is equally likely, then we can find the probability using probability formula. Probability is a chance of prediction. If the probability that an event will occur is "x", then the probability that the event will not occur is "1 - x". If the probability that one event will occur is "a" and the independent probability that another event will occur is "b", then the probability that both events will occur is "ab".

**Probability of an event A**can be written as:

P(A) = $\frac{Number\ of favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

## How to Solve Probability Problems

Steps to find the probability:

Steps to find the probability:

**Step 1:**List the outcomes of the experiment.

**Step 2:**Count the number of possible outcomes of the experiment.

**Step 3:**Count the number of favorable outcomes.

**Step 4:**Use the probability formula.

## Solved Examples

**Question 1:**Two dice are rolled once. Calculate the probability that the sum of the numbers on the two dice is 5.

**Solution:**

Possible outcomes (Sample Space) = {(1, 1), (1, 2),...............,(1,
6), (2, 1), (2, 2),................,(2, 6), (3, 1), (3,
2),...........,(3, 6), .............,(4, 1), (4, 2),..........,(4, 6),
(5, 1), (5,2),...............,(5, 6), (6, 1), (6,
2),......................,(6, 6)}

Total possible outcomes =

Number of outcomes of the experiment that are favorable to the event that a sum of two events is 6

=> Favorable outcomes are: (1, 5), (2, 4), (3, 3), (4, 2) and (5, 1)

Number of favorable outcomes =

Use, probability formula = $\frac{Number\ of favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

= $\frac{5}{36}$

The probability of a sum of 6 is $\frac{5}{36}$.

Total possible outcomes =

**36**

Number of outcomes of the experiment that are favorable to the event that a sum of two events is 6

=> Favorable outcomes are: (1, 5), (2, 4), (3, 3), (4, 2) and (5, 1)

Number of favorable outcomes =

**5**Use, probability formula = $\frac{Number\ of favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

= $\frac{5}{36}$

The probability of a sum of 6 is $\frac{5}{36}$.

**Question 2:**What is the probability of getting head when tossing a coin.

**Solution:**

Sample Space = {H, T}

Number of possible outcomes = 2

Number of favorable outcomes = 1

(because of only one head)

=> Probability of getting head = $\frac{Number\ of favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

= $\frac{1}{2}$

=> Probability of getting head is $\frac{1}{2}$.

Number of possible outcomes = 2

Number of favorable outcomes = 1

(because of only one head)

=> Probability of getting head = $\frac{Number\ of favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

= $\frac{1}{2}$

=> Probability of getting head is $\frac{1}{2}$.