Learn Probability Rules

Probability means chance or possibility. If an event is likely to happen, we say it is probable. On the other hand, if it is not likely to happen, we say it is improbable in this case we say probability is 0. If the event is certain to occur, we say probability is likely 1. In this article we are going to learn the rules of probability.

Probability of an event =number of times an event occurs / total number of outcomes


learning probability rules:


Rule 1:

In all events the value of probability exists between 0 and 1 in this case there are two possibilities. They are

a. An impossible event
b.  A certain event

a. When the value P (A) = 0, the event will not happen as the impossible event when occurred.

       For example: what is probability of getting two head when a coin is tossed?

b. When the value P (A) = 1, the event will occur surely .At a consequence, this rule defines that when A is the event in the given sample space will happen, then the P (A) = 1

        For example: probability of getting head or tail when a coin is tossed.


Other rules of Probability :


Rule 2:

The complement is an occurring event The events in given sample space can be either in the part of event A or can be the part of complement of event A, then probability of event and its complement is added to give the value 1.

P (A) + P (not A) = 1

Rule 3:  either/or Rule :

The occurrence of one event or another event is mean by adding together their individual probabilities , then finding the difference of the probability of both.

P (A or B) = P (A) + P (B) - P (A and B)


Example based on the above rules:


Ex:1 A number is selected at random from 1 to 100 find the probability that it is not a square number.

Sol:  Step 1:Sample space S={1,2,3,4....,100}

n(S) = 100

Step 2:Let `A` be the event of getting square numbers

A ={1,4,9,16,25,36,49,64,81,100}

n(A) = 10

Step 3:P(A) =`(n(A))/(n(S)) = 10/100 = 1/10`

Step 4:The rule discussed above P(A') = 1- P(A)

 `rArr P(A') = 1-1/10 = 9/10`

Thus probability of the number being a non-square number is `9/10`


Practice problems on learning probability rules:


Pro 1: What is the probability of gettting an even number when a die is thrown

Ans: `1/2`

Pro:2 What is the probability that a number sleected from first natural numbers is prime