Recall that two events A and B are conditionally independent given an event C if P(A∩B|C)=P(A|C)P(B|C). Prove that P(A∩B|C)=P(A|C)P(B|C) if and only if P(A|B∩C)=P(A|C).
Recall that two events A and B are conditionally independent given an event C if P(A∩B|C)=P(A|C)P(B|C)....
4. (a) Show that (b) Two events A and B are said to be conditionally independent given C if P(An BIC)P(A|C)P(BC). Prove that if A and B are conditionally independent given C, then
6. Suppose events A and B are conditionally independent given C, which is written ALBIC (a) Show that this implies that ALBIC and ALBIC and ALB-|C, where A means "not A." b) Find an example where ALBIC holds but ALBCE does not hold
7. If A and B are independent events, then P(A and B) equals a. b. c. P(A) + P(B/A). P(A) x P(B). P(A) +P(B). d. P(A/B) +P(B/A) 8.Which formula represents the probability of the complement of event A? b. 1-P(A) c. P(A d. P(A)-1 9. The simultaneous occurrence of two events is called a. prior probability b. subjective probability c. conditional probability d. joint probability 10. If the probability of an event is 0.3, that means the event has a...
1. Consider two independent events, A and B, where 0< P(A) <1,0< P(B)< 1. Prove that A and B' are independent as well.
2.30 Probability of independent events. Given two independent events A and B with PIA 0.3, PB 0.4, find (a) P[AU B; (b) P[AB); (c) P[BIA); (d) P BA)
Given events A and B, (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A will not occur. Express D in terms of A and B. (b) let E be the event that exactly one of the events A or B will occur. Express E in terms of A and B. (c) Use the result in...
If events A and B are independent, then the probability of simultaneous occurrence of event A and event B can be found with ____________. P(A)·P(B) P(A)·P(B|A) P(B)·P(A|B) All of these choices are correct.
Consider two independent events, A and B, where 0くP(A) < 1,0くP(8)く1. Prove that A' and B' are independent as well.
2. Given events A and B (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A wil not occur. Express D in terms of A and B (b) let E be the event that exactly one of the events A or B will occur. Express E in terms (c) Use the result in (a) to find...
Suppose the events A and B are independent. Suppose that P (A) =0 .12 and P (B) =0 .07. What is the probability that only event A occurs?