2.9 a) Suppose that P(AU B) 0.8 and P(A'UB) 0.7. Find P(B). Hint: Fill out a...
6. Given two mutually excdlusive events 4 and B for which PlA)-027 and P(B) 0.46, find (e) P(An B); (f) P(A'n B); (g) P(A'n B); (h) P(A'uB). (c) P(AuB); (d) P(An B); (Hint: Draw a Venn diagram and fill in the probabilities associated with the various regions.)
2./ (HINT: DON'T EVEN TRY THIS WITHOUT DRAWING A VENN DI- 0, BC AGRAM.) W, have ftir events with the following informations: P(AU C) = 0.8, /"(A) = 0.5 P(C) = 0.7 and P(B)--02. AB B. - a./ (4 points) Make a Venn diagram. b./ (4 points) Find P(AC). c./ (4 points) Find P(AC) and P(AB) d./ (4 points) Find P(B1A) and P(C1A).
26. (2pts) Suppose P(AIB) 0.3 and P(B) 0.4. Find P(An B) 0.6, P(B) 0.4, and PAnB) 0.24. Find P(A'n B). Drawing a Venn Diagram may 27. (2pts) Suppose P(A) help.
language, the meaning of conditioning. Suppose P(A) = P(B) = 0.3 and P(A|B) 0.5. Find P(AU B). 2.2 Sunnose P(A) = P(B) = and P(AUB)= p2. Find P(AlB). 2.3
If P(B)=0.2,P(A | B)=0.7,P(B)=0.8, and P(A|B)=0.5, find P(B | A).
2. Given: P(A) = 0.4, P(B) = 0.7, and A and B are independent events. (a) (2 points) Find P(A and B) (b) (2 points) Find PA and B) (b) (c) (3 points) Construct the Venn diagram. А B @ (d) (2 points) Find P(B) (d) (f) (2 points) Find P(A or B) (g) (2 points) Find P(BA) EC
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw the Venn diagram representing AU( B C), (c) For sets A, B and C, draw the Venn diagram representing (AUD) n(B\C). (d) If A and B are two boxes (possibly with things inside), describe the following in terms of boxes A B, P(A), and A.
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)?
b) Assuming the following. P(S)- 0.3 P(BIS) 0.75 P(B)S)-0.20 P(HISnB)-0.20 P(H) Sr. B')= 0.8 P(H S'o B)-0.15 Write out the equations and compute: PSnB)- 0.225 c) Now compute the probabilities pertaining to each section in the Venn diagram 5 :5 2 3:(s л н n в": o.odo d) Write out the equation used and compute P(B'n H). e) Write out the equation used and compute P(H) PCH- 0 Compute the probability that it is snowing, given that I made it...
= 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