1/3, P(B): 1/4, P(AB)-: 1/6, where 1. In a probability space, it is known that P(A)...
3. Suppose that A and B are two events defined over the same sample space, with probabilities P(A) 3/4 and P(B)- 3/8. (a) Show that P(A UB) 2 3/4. (b) Show that 1/8 < P(AB) 3/8 (c) Give inequalities analogous to (a) and (b) for P(A) 2/3 and P(B)1/2.
Let A, B be events such that P(A) = 1/3 , P(B) = 1/4 , and P(AB) = 1/6. Find the following and write in words what events a)-d). Example: AB' means that either A occurs or B does not occur. HINT: draw a diagram. a) P(A' B') b) P(A' B) c) P(A' u B) d) P(A' B') We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
a) What is probability of observing 61325 when rolling fair dice? Probabilities for fair dice: P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6 b) What is probability of observing 61325 when rolling loaded dice? Probabilities for fair dice: P(1)=P(2)=P(3)=P(4)=P(5)= 0.1 and P(6)=0.5 c) What is probability of observing A in a random sequence? d) What is probability of observing ATGC in a random sequence? e) What is probability of observing ATGC in a genome described by a simple model where P(G)=P(C)=0.33 and P(A)=P(T)=0.17 i.e. P(ATGC | simple...
The following applies to questions 4-6 below. Assume the following notation: p(A) is the probability of event A; P(AB) is the probability of A and B; p(AVB) is the probability of A or B; p(AB) is the probability of A given B; S is the universe of possibilities; -A is the negation of A; and is the null event. 4. p(AB) where xis A. p(A) P(B) B. P(AlB)p(B) C. p(BIA) D. p(B)2 E. p(A V B) 5. For all A...
P(B |A) = .6 P(B) = .4 P(A) = .6 where P indicates probability a. Are A and B independent b. Are A and B exclusive c. Calculate P(A and B) d. Calculate P(A | B)
Assume that (Ω, B, P) is a probability space, where Ω = [0, 1) and P(B) = ?B 1dω, ∀B ∈ B.1 Bisaσ-fieldthatcontainsallopenandclosedsub-intervalsof[0,1)andtheircount- able unions and intersections.2 Assume A1 = [0, 1/2), A2 = [0, 1/4) ∪ [1/2, 3/4), A3 = [0, 1/8) ∪ [1/4, 3/8) ∪ [1/2, 5/8) ∪ [3/4, 7/8), determine whether or not {A1, A2, A3} is an independent set. Moreover, determine whether or not it is pairwise independent.3
4 PROBABILITY (16) An experiment consists of tossing a fair coin (head and tail T) three times. The sample space S in this experiment is S - (HT), and a possible event Ecould be E = {H,H). (1) True. (2) False (17) Which of the following statements is true? (1) The set of all possible events of an experiment is called the sample space, S. (2) If an experiment is performed more than once, one and only one event can...
Consider the sample space S = {-3,-1, 0, 2, 4} and the events A = {-1, 0}, B = {0, 2}, and C = {-3, 0, 4} derived from the discrete random variable X. Let the probability of each outcome be as listed in the table below. Outcome (X) Probability −3 0.10 −1 0.20 0 0.30 2 c 4 0.25 Outcome (X) l Probability -3 0.10 -1 0.20 0 0.30 2 c 4 0.25 a) Find the value of the...
Let A and B be events with probabilities P(A)-3/4 and P(B)-1/3 (a) Show that 12 3' (b) Let P(AnB) - find PA n Bc).
Two events A and B are such that P(A)2, P(B).3, and P(AUB) -4. Find following: a P(An B) b P(AUB) d P(AB) If A and B are independent events with P(A)and P(B) .2, find the following: a P(AUB) b PAnB) c P(AU B)