Search 75,638 tutors
FIND TUTORS
Ask a question
1 0

Joint Probability: Let P(A) = .3, P(B) = .4 and P( A U B ) = .7 a. What is the joint probability of A and B? b. Find the probability of the complement of A.

Tutors, please sign in to answer this question.

2 Answers

The union  probability of the events A and B is
 
             P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.4 - P(A∩B) = 0.7 according to the text.
 
Thus, P(A∩B) = 0, or two events, A and B, do not intersect.
 
The probability of the compliment of A is 1 - P(A) = 0.7. 
a) The joint probability is P(A ∩ B), which satisfies
 
P( A ∪ B ) = P(A) + P(B) - P(A ∩ B)
.7 = .3 + .4 - P(A ∩ B)
So, P(A ∩ B) = 0
 
b) P(not A) = 1 - P(A) = 1-.3 = .7

Seattle tutors