An experiment can result in to one of the following 5 outcomes E1, E2, E3, E4, and E5 with probabilities: P(E1)=0.2 P(E2)=0.3 P(E3)=0.15 P(E4)=0.25 P(E5)=0.10 Define the following 3 events: A={E1, E3, E4) B={E2, E3} C={E2, E5} Find the following probabilities: P(A) P(B) P(A∩B) P(A∪ B) P(A∪C)

Consider two events following receiving a bachelor’s degree from a prestigious university: A = {being accepted into a graduate program} and B = {receiving a job offer}. We know the following is true: P(A) = P(B) = 0.7 P(A|B) = 0.9 Are events A and B independent? Why or why not?

In which of the following circumstances are the events A and B independent? 0 a. P(A) = 0.35, P(B) = 0.63, P(AnB ) = 0.32 gb. P(A) = 1/2, P(8) = 21/55, P(AnB) =3/22 O c. P(A) = 1/2, P(B) = 1/2, P(AnB) = 1/4 © d. P(A) = 0,7, P(A/B) = 0,9 Премахване на моя избор

An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.