If P(B)=0.2,P(A | B)=0.7,P(B)=0.8, and P(A|B)=0.5, find P(B | A).
Answer:
Given P(B)=0.2,P(A|B)=0.7,P(B')=0.8, and
P(A|B')=0.5
P(A)= P(A∩S)
= P[A∩(BUB')]
= P[(A∩B) U (A∩B')]
= P(A∩B) + P(A∩B')
= P(A|B)P(B) + P(A|B')P(B')
= (0.7)(0.2) + (0.5)(0.8)
= 0.54
P(B|A) = P(A∩B)/P(A)
= 0.7*0.2/0.54
=0.2592
If P(B)=0.2,P(A | B)=0.7,P(B)=0.8, and P(A|B)=0.5, find P(B | A).
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,
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...
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
The events A and B are mutually exclusive. If P(A) = 0.7 and P(B) = 0.2, what is P(A or B)? O A. 0.5 OBO OC. 0.9 OD. 0.14
For two events, A and B, P(A)=0.2, P(B)=0.5 and P(A|B=0.2. a. Find P(A∩B)= b. Find P(B|A).=
If, P(A∪B)=0.7, P(A)=0.2, and P(A∩B)=0.15 find P(B). Assume that A and B are events.
If P(A)=0.7 and P(B)=0.4 and P(A and B)=0.2 then P(A and B9= Select one: O a. 0.5 b. 0.56 O c.0.9 d. 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
Suppose that P(A) = 0.2 and P(B) = 0.5 and P(A ∪ B) = 0.6. Find P(A' ∪ B' )
Is the Markov chain time reversible? Provide details.
0.7 0.2 0.1 0.2 0.6 0.2 0.1 0.4 0.5
0.7 0.2 0.1 0.2 0.6 0.2 0.1 0.4 0.5