For this problem, assume that Pr[A∪B]=0.65Pr[A∪B]=0.65 and Pr[A]=0.45Pr[A]=0.45.
(1) What is Pr[B] if A and B are independent events?
(2) What is Pr[B] if A and B are disjoint events?
For this problem, assume that Pr[A∪B]=0.65Pr[A∪B]=0.65 and Pr[A]=0.45Pr[A]=0.45. (1) What is Pr[B] if A and B...
The probability that the event A occurs is Pr( A ) = 1/3 and the probability that the union event A∪B occurs is Pr( A∪B ) = 5/6. Answer the following questions. 1. If the events A and B are disjoint, what is the value of Pr(B)? 2. If the events A and B are independent, what is the value of Pr(B)? (*Answer in the decimal form, not in the fractional form.) Thank you so much!
independent events A and B in a sample space S, but assume that Pr[A]=0.3 and Pr[B]=0.15. Compute the following conditional probabilities: (1) Pr[A|B]= equation editorEquation Editor (2) Pr[B|A]= equation editorEquation Editor
Suppose E and F are independent events. Find Pr[E′∩F] if Pr[E]=1/3 and Pr[F]=1/3 A and B are independent events. If Pr(A∩B)=0.24 and Pr[A]=0.3, what is Pr[B]?
E, F, and G in a sample space S. Assume that Pr[E]=0.5, Pr[F]=0.45, Pr[G]=0.55, Pr[E∩F]=0.3, Pr[E∩G]=0.3,and Pr[F∩G]=0.25. Find the following probabilities Pr[E∪F] = Pr[F′∩G]= Pr[E′∩G′]=
1. Consider a Markov process with 2 states A and B, and transition probabilities Pr[A-> A] 0.3, Pr[A B-07, Pr(B+ B-06, Pr[B-A-0.4 . Assume that at time t-0 we have PrlA] 8, and Pr B-2 a) What are Pr[A], and Pr B] at time t-1,2,3? b) Prove that PriA] +Pr[B 1 at each time step. c) Find the limit of Pr[A] when t- > oo. 1. Consider a Markov process with 2 states A and B, and transition probabilities Pr[A->...
Problem # 1: Prove that Pr(AB)-1-Pr(A, 1B). Problem#2: Show that if E and F are independent, then E ' and F are independent.
Problem 1. A biased coin with probability plandin with a Heads is lipped 4 times. (a) Define the basic random variables and give the sample space and assign probabilities to the outcomes. (b) Let X be the total number of Heads in the four flips Draw a Venn diagrain showing the five events X = ii 0,1,2,3,4 as well as the sample space and the outcomes. Is X a random variable? c) Are the events X 1 and X 2...
A and B of a sample space S, but assume that Pr[A]=0.2 and Pr[B]=0.6. Find Pr[A∪B] under each of the following conditions: (1) If A⊂B, then Pr[A∪B]= (2) If A∩B=∅, then Pr[A∪B]= (3) If A∩B′=∅, then Pr[A∪B]=
generate the following sequence of random numbers between 0 and 1 0.55, 0.89, 0.62, 0.45, 0.65, and .78
Problem 3: If P(A) 0.2, P(B) 0.1, and P(A or B) PIA U B) 0.28, then (a) (2.5 points) find the P(A and B). That is, find P(AnB). (b) (2 points) clearly explain whether the events A, B are mutually exclusive (disjoint). (c) (2 points) clearly explain whether the events A, B are independent based on probability