• Support PF! Buy your school textbooks, materials and every day products Here!

Probability of events

  • #1
I'm having difficulty time of trying to figure out answer.

Question:
P(A^c U B) = 0.6
P((A^c U B^C) = 0.8
Find P(A) ?

Sol:
P(A^c U B) = P(A^c) + P(B) - P(A^c Intersection B)
P(A^c U B^c) = P(A^c) + P(B^c) - P(A^c Intersection B^c)
0.6 + 0.8 = 2*P(A^c) + 1 - P(A^c) <==== HOW ?????????
P(A^c)=0.4, P(A)=1-P(A^c)=0.6

PROBLEM:
I have the solution, but I don't get how he got "- P(A^c)"
I think my instructor skipped some steps.
 
Last edited:

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
it should be clear it you write out the steps
[tex] P(A^c \cup B) = P(A^c) + P(B) - P(A^c \cap B) [/tex]
[tex] P(A^c \cup B^c) = P(A^c) + P(B^c) - P(A^c \cap B^c) [/tex]

now add them together
[tex] P(A^c \cup B^c) + P(A^c \cup B) = 2P(A^c) + (P(B^c)+P(B)) - (P(A^c \cap B^c) +P(A^c \cap B) )[/tex]

now see if you can fill in the last bit
 

Related Threads on Probability of events

  • Last Post
Replies
5
Views
2K
Replies
4
Views
3K
Replies
5
Views
1K
Replies
2
Views
10K
  • Last Post
Replies
1
Views
320
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
21
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
18
Views
5K
Replies
1
Views
8K
Top