TOPIC:Conditional law of probability.
2. a) Let A and B be two events such that P(A) 4, P(B) .5 and P(AnB) 3 Find P(AUB). b) Let A and B be two events such that P(A)-5, P(B) 3 and P(AUB) .6. Find P(An B)
(1) Suppose that A and B are events with P[A] = 0.4 and P[B] = 0.7. Show that 0.1 < PAB < 0.4. Justify your answer clearly. P(ANB) - PCA) PCB) = 0.4.0.7 = 0.28 with 0.15 0.28 <0.4 PLA) occuring 04 P(B) occuring 0.7 P of both events occuring at the same time should be = 0.28 which is in Ran 0,4 1028 0.7 2/10
Let PA) = 0.40, AB) = 0.40, and AAN B) = 0.18. a. Are A and B independent events? O Yes because AAB) = PA). Yes because AAN B) + 0. O No because PAB) AA). O No because AAN B) 0. b. Are A and B mutually exclusive events? Yes because RAIB) = AA). Yes because AAN B) 0. O No because PAB) # AA). b. Are A and B mutually exclusive events? O Yes because AAB) = PA)....
Let A and B be two disjoint events such that P(A) = 0.29 and P(B) = 0.36. What is P(A and B)?
Let A and B be two disjoint events such that P(A) = 0.25 and P(B) = 0.45. What is P(A or B)?
Let P(A) = 0.4 P(B) = 0.5 P(A|B) = 0.2 (Please show working). If the events a and b are independent, calculate the P(A and B) If the events a and b are not independent, calculate the P(A and B) If the events a and b are mutually exclusive, calculate the P(A or B)
Problem #3: Let A and B be two events on the sample space S. Then show that a. P(B) P(AOB)+P(AnB) b. If Bc A, then show that P(A)2 P(B) Show that P(A| B)=1-P(A|B) C. P(A) d. If A and B are mutually exclusive events then show that P(A| AUB) = PA)+P(B) Problem 4: If A and B are independent events then show that A and B are independent. If A and B are independent then show that A and B...
Let A and B be two events such that P(A)=0.40, P(B)=0.5 and P(A|B)=0.4. Let A′ be the complement of A and B′ be the complement of B. (give answers to two places past decimal) 1. Compute P(A′). 2. Compute P (A ∪ B). 3. Compute P (B | A). 4. Compute P (A′ ∩ B).
Let A and B be events with probabilities not equal to 0 or 1. Show that if P(B|A) = 1, then P(A0 |B0 ) = 1. You may use the axioms of probability, all the theorems from the notes, and anything that was proven on the homework or in the notes. Hint: Consider slide 9 in chapter 4 for event A and show that P (A|B0 ) = 0.
[1] The joint probability mass function of two discrete random variables A and B is Pab(a,b) = {ca?b, Sca²b, a= -2,2 and b = 1,2 otherwise Clearly stating your reasons, answer the following two (i) Are A and B are uncorrelated? (ii) Are A and B independent?