**Introduction
**

** **The **probability **of an incident is a proportion that tells how possible. it is that an event will take place. The numerator is the number of favorable outcomes and the

Denominator is the number of possible outcomes.

**Probability : ***number of flattering outcomes *

**/**

*number of possible outcomes*

* ***Probability** is we can try to measure the chances of it occurrence.

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## Subjective probability Explanation:

Here we will explain the subjective probability.

Numerical measure of the likelihood of an event to occur . If an observation which has n possible ways exhaustive and mutually exclusive and out of them in m ways in the event. A occurs, then the probability of occurrence of the event.

A is given by P(a = m/n.

If in a random sequence of n trials of an event, M are favorable to the event , the probability of that event occurring is the limit of the ratio M/n, when n is very very large , this lies between 0 and 1 .

P(a)=0 means that the event can not take place.

P(a)=1 means the event is bound to occur .

the events,A2,A3……..An are said to the mutually exclusive if ,

P(A_{i} ∩ A_{j})=0 for i=1,2,3,……n.

J=1,2,3,…….n, I ≠ j

He events are said to be exhaustive if

P(A_{1})+ P(A_{2})+ P(A_{3})_………. P(A_{n})=1 if ,

A ∩ B ≠ 0 then

P(A υ B)=P(A)+ P(B)

And if A ∩ B ≠ 0v then

P(A υ B)=P(A)+ P(B)-P(A B)

## Subjective probability Example:

1. When you toss a coin , there are two ways it can fall. The subjective probability of getting a head on one roll of a coin is one chance out of two .

**Solution:**

P(h) means the probability of getting a head on one toss of a coin.

P(t) means the probability of getting a tail on one toss of a coin.

**Step 1 : **the *number of favorable outcomes for * head** =1**

**Step 2 : **the *number of favorable outcomes *for tail** =1**

**Step 3 :** *number of possible outcomes =2*

**Step 4 :** the probability of the event for head** =*** number of favorable outcomes *

**/**

**number of possible outcomes****Step 5 : **the probability of the event for head= P(h)=n(e)/n(s)

**Step 6 : **the probability of the event for head=1/2

**Answer : 1/2**

The above problem is sample of subjective probability problem.

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