Consider three random events, A, B and C. Suppose that P(A) = 0.5, P(A∩C) = 0.2, P(C) = 0.4, P(B) = 0.4, P(A∩B∩C) = 0.1, P(B∩C) = 0.18, and P(A∩B) = 0.21. Calculate the following probabilities:
c. P((B∩C)c ∪(A∩B)c)
Consider three random events, A, B and C. Suppose that P(A) = 0.5, P(A∩C) = 0.2,...
= 0.3. Consider events A and B such that P(A) = 0.7, P(B) = 0.2 and P(ANB) Compute the probability that A will occur, given that B does not occur, A. 0.4 B. 0.1 C. -0.1 D. 0.5 E. none of the preceding
Consider the following Transition Matrix, T: From A B C A B C 0.2 0.5 0.3 0.3 0.3 0.4 0.5 0.1 0.4 Find the following probabilities: a.) moving from state A to state C b.) moving from state B to state A c.) remaining in state C
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)
Suppose that P(A)0.5, P(B)0.2, P(C) 0.3, P(AnB) 0.1 and P(AnC) 0.1. Compute the following: (a) (2 points) P(AUB) b) (6 points) P(A UC) (c) (4 points) Are the events A and B independent? What about A and C? (d) (8 points) If the sets B and C are mutually exclusive sets, what is P(A U B U C)?
A 0.2 В 0.5 0.1 Given the events A and B above, find the following probabilities P(A and B) P(A or B) P(A | B) P(B | A) = P( not A and B) = P(A and not B) Are events A and B independent (yes Explain why or why not or no) Are events A and B independent (yes Explain why or why not or no) GRB 5/5/2019 Math 121 Final Spring 2019
p(b)= 0.5, p(c)=0.2, events b and c are mutually exclusive. find p( b intersects c)
0.7 0.2 0.1 0.2 0.6 0.2 0.1 0.4 0.5 Check the time reversibility π,B- π, P, 0.7 0.2 0.1 0.2 0.6 0.2 0.1 0.4 0.5 Check the time reversibility π,B- π, P,
1. Random Walk: Consider a random walk described by the following probability rules: P(+x) 0.5; P(-x) 0.1; P(ty) 0.2; P(-y) 0.2 (a) Is the walk biased? If so in which direction? Explain. (b) Compute the following for N steps if the step size is equal to a: <x>, <y>, <x>, <y (c) After long time (after large number of steps, where would the object be found? (find σ, and 1. Random Walk: Consider a random walk described by the following...
A and B are two events such that P(A) = 0.4, P(B) = 0.5, and P(A|B) = 0.3. Find P(A and B). Select one: a. 0.6 b. 0.15 c. 0.12 d. 0.2
0.2 Question 7 (1 point) <Venn 3> There are 2 events: A, B with P(A)-0.5, P(B)-0.4, P(AUB)-0.7 Find P(BA) (2 decimal places without rounding-up) Question 8 (1 point) Saved <Venn 4>