Home
Arithmetic
Algebra
Geometry
Statistics
Probability
Set Theory
Trigonometry
Matrices
Vectors
Calculus
SAT Preparation
ACT Preparation
GMAT Preparation
Interactive Zone
Math Worksheets
Math Games
Fun Games
Math Trivia
English Help
Chemistry
Animal Facts
Tutoring Services
What's New
Links

 

Probability Diagrams (or Possibility Diagrams)

When an experiment is more complex constructing a probability diagram or possibility diagram may be helpful.

 

 

Example:

The diagram shows two spinners, each of which is divided into 4 equal sectors. Each spinner has a pointer which, when spun, is equally likely to come to rest in any of the four equal sectors.


In a game, each pointer is spun once.

Find the probability that
a) the pointers will stop at the same number
b) the first spinner shows the larger number.

Solution:

Construct the probability diagram. Each dot represents a possible outcome according to the coordinates.


a) Let A = event of getting the same number on the two spinners.

From the probability diagram, n(A) = 4, n(S) = 16

P(A) =

b) Let B = event the first spinner shows the bigger number.

From the probability diagram, n(B) = 6

P(B) =

 

 

Example:

Two fair dice are thrown together. Find the probability that the sum of the resulting number is
a) odd
b) a prime number

Solution:

Construct the following probability diagram showing the sums:

a) Let A be the event that the sum is odd

From the probability diagram, n(A) = 18

P(A) =

b) Let B be the event that the sum is a prime

Count the number of 2, 3, 5, 7 and 11 in the probability diagram.

n(B) = 15

P(B) =

 

 

Example:

X = {1, 2, 3} and Y = {4, 5, 6}. An element x is selected from X and an element y is selected from Y.

Complete the following probability diagrams for x + y and x × y

a) Find the probability that the sum x + y is:
i) prime
ii) greater than 7

b) Find the probability that the product xy is:
i) odd
ii) at most 10

Solution:

a) The following probability diagrams for x + y and x × y

a) The probability that the sum x + y is:

i) prime

Let S be the sample space, and A be the event that the sum is prime.

From the probability diagram, n(A) = 4 ; n(S) = 9

P(A) =

ii) greater than 7

Let S be the sample space, and B be the event that the sum is greater than 7.

From the probability diagram, n(B) = 3 ; n(S) = 9

P(B) =

 

b) The probability that the product xy is:

i) odd

Let S be the sample space, and C be the event that the product is odd.

From the probability diagram, n(C) = 2 ; n(S) = 9

P(C) =

ii) at most 10

Let S be the sample space, and D be the event that the product is at most 10.

From the probability diagram, n(D) = 5 ; n(S) = 9

P(D) =

 

 

The following video shows another example of using diagrams to help solve probability problems.

 

 

 

Custom Search

 

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

 

© Copyright 2005, 2008 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.


 

 

Custom Search