Finite Math
posted by Preet .
Let A,B be events in a sample space. you are given the following probabilities:
P(A)=0.8, P(BA)=0.3, P(BA^c)=0.8
Find:
1) P(B)
2) P(AB)
3) P(A^cB^c)

Finite Math 
MathMate
In the following, A' will be used in place of A^{c} for ease of typography.
(1) since A and A' are partitions of A, we can apply the law of total probability
P(B)=P(BA)*P(A)+P(BA')*P(A')
(2) Use Bayes Theorem
P(AB)
=P(A∩B)/P(B) ... def of cond. prob
=P(B∩A)/P(B) ... commutativity
=[P(BA)*P(A)]/P(B) ... def of cond. prob
(3) We need to use
P(A'∩B')=1P(A∪B) ... complement
and
P(A∪B)=P(A)+P(B)P(A∩B) ... prob. of union of sets
P(A'B')
=P(A'∩B')/P(B') .. def of cond.prob
=(1P(A∪B))/(1P(B)) ... compl
=(1P(B∪A))/(1P(B)) ... commutativity
=[1(P(A)+P(B)P(A∩B)]/(1P(B)) ... union of sets
=[1(P(A)+P(B)P(B∩A)]/(1P(B)) ... commutativity
=[1(P(A)+P(B)P(BA)*P(A)]/(1P(B)) ... def. of cond. prob.
Please check and understand every line. Post if you have questions.
Respond to this Question
Similar Questions

math
Assume that your sample space is S = {O1, O2, O3, O4, O5, O6 } with associated weights (probabilities) w1 = 0.15, w2 = 0.25, w3 = 0.10, w4 = 0.20, w5 = 0.15, and w6 = 0.15. Determine the probability of the following events: {O3 }∩{O5 … 
Probability
Let A and B be events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A B) = 0.27. Find the probabilities below P(AB) 
Math
Given that a sample space is discrete if it contains either a finite number of points or a countably infinite nunber of points and a sample space is continuous if it contains uncountable number of points 1) if two distinct points on … 
statistics
A and B are events defined on a sample space, with the following probabilities. Find P(A and B). (Give your answer correct to two decimal places.) P(A) = 0.5 and P(B  A) = 0.4 
math
A and B are events defined on a sample space, with the given probabilities. Find P(A and B). (Give your answer correct to two decimal places.) P(A  B) = 0.43 and P(B) = 0.75 
Math/Statistics
Suppose that A and B are events defined on a common sample space and that the following probabilities are known. Find P(A or B). (Give your answer correct to two decimal places.) P(A) = 0.32, P(B) = 0.36, P(A  B) = 0.24 
Math/Statistics
Suppose that A and B are events defined on a common sample space and that the following probabilities are known. Find P(A or B). (Give your answer correct to two decimal places.) P(A) = 0.32, P(B) = 0.36, P(A  B) = 0.24 
Math/Statistics
A and B are events defined on a sample space, with the given probabilities. Find P(A and B). (Give your answer correct to two decimal places.) P(A  B) = 0.43 and P(B) = 0.75 
Statistics
Suppose that A and B are events defined on a common sample space and that the following probabilities are known. Find P(A or B). (Give your answer correct to two decimal places.) P(A) = 0.34, P(B) = 0.41, P(A  B) = 0.2 
Finite Math
Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.6, and P(A intersection B) = 0.15. Find the probabilities below. Hint: (A intersection Bc) union (A intersection B) = A. (a) P(ABc) ________ (b) P(BAc) …