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# 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.

Also, how do you differentiate between solving them as a dependent or an independent event?

Let P(A) = .3, P(B) = .4 and P( A ∪ B ) = .7

a. What is the joint probability of A and B?
b. Find the probability of the complement of A.

### 2 Answers by Expert Tutors

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
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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.
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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