To understand how to solve probability using the laws

S is a sample space of a random experiment then Any task of the probability events that must be satisfies the three basic laws of probability.

P(A) “0. Where A is for any event.

P(s)=1

P(AUB)=P(A)+P(B) where A and B are two Mutually Exclusive event

Example for understanding how to solve laws of probability :

A event is a subset of the sample space S.

For Example: If A be the event then the sum of their numbers are 8 in the dice.Finrd the probability for getting 8?

Solution for solve law of probability:

A={(2,6),(3,5),(4,4),(6,2)}

It is same as the outcome of rolling as (2,6) OR (3,5) OR (4,4) OR (6,2).

Then the Law for the mutually Exclusive event for addition then the Probability for happening the event A is=

P(A)= P(2,6)+P(3,5)+P(4,4)+P(6,2)

= 1/36+1/36+1/36+1/36

= 1/36.

Basic Laws of Probability Used to Solve Problems :

Basic laws used to solve probability

The sample space is made up of A+’barA’

A+’barA’ = Whole sample space.

Example for solve law of probability: Find ‘barA’ for the probability of occouring 0.4 in the event A

Solve using the basic law of probability:

P(A)= 0.4

P( ‘barA’ )=1-P(A)

=1-0.4 =0.6.

Union Law:

P(AUB)=P(A)+P(B)-P(AnB)

Ex:Solve using the union law of probability P(A)=0.46 P(B)= 0.58 P(A”B)=0.66

Solution:P(AUB)= P(A)+P(B)-P(A”B)

=0.46+0.58-0.66

=0.38

Mutually Exclusive Events:

If the events A and B does not have any common outcomes then they are called mutually Exclusive.

P(AUB)=P(A)+P(B)

Conditional Probability and Independence:

Assume the event A/D

Where D is the outcome of the event to rolling a dice.The possible outcomes of the sample space is 16outcomes that are listed in the event D.and 2 of those two outcomes are also in the event A.The events A and B are made by these two outcomes.so the probability for the events A/D is in the ratio of the outcomes that are present in A and D to the Number of outcomes in D.

P(A/D)='(2)/(16)’ ='(1)/(8)’

Solve the Example Using Laws of Probability

John draws a balls from a bag Containing 14 balls. There are 4 violet balls 5 pink balls 6 white balls. What is the probability to john draw a pink balls?

Solution:P (pink balls)= number of pink balls/ total number of balls

= 5/14

probability = 0.35