= 0.3. Consider events A and B such that P(A) = 0.7, P(B) = 0.2 and...
1. (15pts) Events A, B and C are such that P(A) = 0.7, P(B) = 0.6, P(C) = 0.5, P(AnB) = 0.4 , P(AnC) = 0.3, P(BnC) = 0.2, P(AnBnC) Find (a) either B or C happens (b) at least one of A, B, C happens; c) exactly one of A, B, or C happens. 0.1.
Consider two events A and B. It is known that P(A) = 0.3, P(B|A) -0.2 and Calculate the following. Enter your answers to at least four decimal places accuracy. P(B|AC) = 0.3. (a) P(AC) - $ (b) P(B) - (c) P(ANB) (d) P(AB) = 3
4. Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0,4 (a) Can events A and B be mutually exclusive? Explain. | (b) If P(A and B) = 0.2, compute P(A or B). 3. Basic Computation: Multiplication Rule Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(AIB) = 0.1, compute P(A and B). 6. Basic Computation: Multiplicat (a) If A and B, are independent...
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)?
Suppose that A and B are mutually exclusive and complementary events, such that P(A)=0.7 and P(B)=0.3. Consider another event C such that P(C/A)-0.2 and P(C/B)=0.3. What is P(C)?
intelligent control systems fuzzy logic based contril 0.8 0.7 04 0.3 0.2 0.3 b) Plot the ou a) Plot the output: -BUB 1.0 0.9 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.5 0.4A 0.3 0.2 0.2 0.17 0.1 c) Determine the defuzzified output y, by using I. Center of Gravity Method (COG) Height Method (H) II. + 1 (0.5)+3 05)+ 5(0.1) 6() 0.8 0.7 04 0.3 0.2 0.3 b) Plot the ou a) Plot the output: -BUB 1.0 0.9 0.9...
(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
Two events A and B are such that P(A) = 0.4, P(B) = 0.5, and P(AUB) = 0.7. (a) Find P(A n B). 0.2 (b) Find P(AUB). 0.8 (c) Find P(An B). 0.3 (d) Find P(AB). (Enter your probability as a fraction.) 1/2
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,
Consider the following probability distribution: x P(x) 1 0.1 2 ? 3 0.2 4 0.3 What must be the value of P(2) if the distribution is valid? A. 0.6 B. 0.5 C. 0.4 D. 0.2 What is the mean of the probability distribution? A. 2.5 B. 2.7 C. 2.0 D. 2.9