Is the Equation P(A' U B) = P(B) + P(A' U B') Correct in S1 Statistics?

  • Context: High School 
  • Thread starter Thread starter Googl
  • Start date Start date
  • Tags Tags
    Probabilities
Click For Summary
SUMMARY

The equation P(A' U B) = P(B) + P(A' n B') is incorrect in S1 statistics; it should be P(A' U B) = P(B) + P(A' n B). A Venn diagram can effectively illustrate this relationship, where A' is represented as C. The correct interpretation involves recognizing that C n B' equals C - B, which clarifies the disjoint sets involved.

PREREQUISITES
  • Understanding of basic probability concepts, including unions and intersections.
  • Familiarity with Venn diagrams for visualizing set relationships.
  • Knowledge of notation used in probability, such as A' for the complement of A.
  • Experience with S1 statistics curriculum and terminology.
NEXT STEPS
  • Study the principles of set theory and probability, focusing on unions and intersections.
  • Learn how to construct and interpret Venn diagrams for complex probability problems.
  • Review the properties of complements in probability, specifically how they relate to unions and intersections.
  • Explore additional examples of probability equations to solidify understanding of notation and operations.
USEFUL FOR

Students revising S1 statistics, educators teaching probability concepts, and anyone seeking to clarify the relationships between probability equations and set theory.

Googl
Messages
111
Reaction score
1
Hi all,

Could you confirm this for me please. I am revising S1 statistics.

P(A' u B) = P(B) + P(A' u B')

Is that true?

I assume you can represent that on a venn diagram. Is that true.

I am having trouble understanding the equations which contain ' such as P(A' n B).

Thank you.
 
Physics news on Phys.org
Googl said:
Hi all,

Could you confirm this for me please. I am revising S1 statistics.

P(A' u B) = P(B) + P(A' u B')

Is that true?

I assume you can represent that on a venn diagram. Is that true.

I am having trouble understanding the equations which contain ' such as P(A' n B).

Thank you.
The equation is correct, except for A'uB', which should be A'nB'.
If you want to make a Venn diagram, I suggest that you let C = A'.
CuB = B + CnB' (disjoint jets). You may be more comfortable using CnB' = C-B.
 

Similar threads

Undergrad How far and how close to p=0.05 for statistical significance?
  • · Replies 24 ·
Replies
24
Views
6K
Undergrad Proper understanding of p-value
  • · Replies 5 ·
Replies
5
Views
2K
High School Relative And Absolute Probability (Probability Of Picking A Red Ball)
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad What Are the Key Differences Between OLS and GLM Models in Statistical Analysis?
  • · Replies 3 ·
Replies
3
Views
3K
High School How to calculate this conditional probability?
  • · Replies 7 ·
Replies
7
Views
866
Undergrad Understanding extinction probability in simple GWP
  • · Replies 1 ·
Replies
1
Views
2K
High School Intuitive explanation for P(A U B) = P(A) + P(B)
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding the P(B|A) ≡ P(A ∩ B) / P(A) formula.
  • · Replies 16 ·
Replies
16
Views
4K
High School Cant get Venn diagram to agree with Demorgan's Law
  • · Replies 10 ·
Replies
10
Views
3K