SOLUTION: This is the question: For 2 events A and B defined on a sample space S,
N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2. Given that
N(S)= 120, how many outc
Algebra.Com
Question 470498: This is the question: For 2 events A and B defined on a sample space S,
N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2. Given that
N(S)= 120, how many outcomes belong to neither A Nor B?
This is a sample space and algebra of sets problem. I'm not sure where to start.
Thanks.
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For 2 events A and B defined on a sample space S,
N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2. Given that
N(S)= 120, how many outcomes belong to neither A Nor B?
------------
Draw 2 intersecting circles; label them A and B.
---
Draw a rectangle around the circles ; label it S=120
---
Put "2" in the intersection of A and B.
---
Put "15" in the part of A that is not in the intersection.
Put "50" in the part of B that is not in the intersection.
----
Now you see there are 15+2+50 = 67 in A or B.
---
Therefore there are 120 - 67 = 53 in S that are not in A or B.
=====================
Cheers,
Stan H.
==============
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
N(A) = N((A and B') U (A and B)) = N(A and B') + N(A and B) = 15 + 2 = 17
N(B) = N((A' and B) U (A and B)) = N(A' and B) + N(A and B) = 50 + 2 = 52
==> N( A U B) = N(A) + N(B) - N(A and B) = 17 + 52 - 2 = 67
==> N((A U B)') = N(S) - N(A U B) = 120 - 67 = 53.
RELATED QUESTIONS
This is the question: 2 events, A and B, are defined on a sample space S such that... (answered by robertb)
Given 2 events A and B within the sample space S; P(A/B)=n(A and B)/n(B)
Use this... (answered by stanbon)
Find the following probabilities:
(A) Events A and B are mutually exclusive events... (answered by stanbon)
Find the following probabilities:
A)Events A and B are mutually exclusive events... (answered by stanbon)
let s=a,b,c,d,e,f be a sample space of an experiment and let e = a,b f =a,d,f and g... (answered by user_dude2008)
Events A, B, and C are defined on sample space S. Their corresponding sets of sample... (answered by stanbon)
Events A, B, and C are defined on sample space S. Their corresponding sets of sample... (answered by Fombitz)
Find the following probabilities:
(A)Events A and B are mutually exclusive events... (answered by jrfrunner)
7. Which of the following is a characteristic of a binomial probability experiment?
A.... (answered by stanbon)