Probability rules, Mathematics

Probability Rules

A probability is a number assigned to the occurrence of an event in a sample space. Probability measures must satisfy three rules. If A is an event with probability denoted by P(A), then the following rules hold:

Rule 1

The probability of the entire sample space S is 1, i.e. P(S) = 1.

29_probability rules.png

Area of sample space rectangle = 1. An event A is represented within the rectangle. Minimum possible area of A is 0 and maximum possible area is 1.

Rule 2

The probability of the event A must be greater than or equal to 0 and less than or equal to 1 or 100%, i.e. 0 < P(A) < 1. This rule says that probabilities cannot be negative and as the probability of the sample space is 1, the probability of an event contained in the sample space should be less than or equal to 1.

Rule 3

If A and B are mutually exclusive events, then the probability of (A or B) is equal to the sum of the probabilities of A and B.

P(A or B) =  P (A) + P (B) because P (A and B) = 0 as A and B are mutually exclusive.

Mutually exclusive events are those which do not overlap when represented in Venn diagrams.

1844_probability rules1.png

A & B are mutually exclusive events

C and D are not mutually exclusive events

Two events A and B are mutually exclusive if the occurrence of one implies the non-occurrence of the other. Hence obtaining a head on tossing a coin and obtaining a tail are mutually exclusive events.

Posted Date: 9/14/2012 4:25:18 AM | Location : United States







Related Discussions:- Probability rules, Assignment Help, Ask Question on Probability rules, Get Answer, Expert's Help, Probability rules Discussions

Write discussion on Probability rules
Your posts are moderated
Related Questions
Can you explain that it is true that a line that slopes downward from left to right has a positive slope?

a recipe good for 4 servings require 1/8 tsp. black pepper and 1/2 tsp. of salt. how much black pepper and how much salt needed for 2 servings?


It’s been a busy weekend for Larry. Five people in his neighborhood left on vacation Saturday morning and each of them left a pet for Larry to care for until they return. It’s a go

more questions on wavy curve method

A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx

Let A be an n×n matrix. Then Show that the set U = {u?R^n : Au = -3un} is a Subspace of R^n

Next we have to talk about evaluating functions.  Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at

The scores of students taking the ACT college entrance examination are normally distributed with a mean µ = 20.1 and a standard deviation σ = 5.8. a)    A single student is sele