Suppose A,B, and C are events such that: P(A)=P(B)=P(C)=0.3, P ( A ) = P ( B ) = P ( C ) = 0.3 , P(AB)=3P(ABC), P ( A & B ) = 3 P ( A & B & C ) , P(A∪C)=P(B∪C)=0.5, P ( A ∪ C ) = P ( B ∪ C ) = 0.5 , and P(AcBcCc)=0.48. P ( A c & B c & C c ) = 0.48 . Sketch a Karnaugh map showing the probabilities of different sets. What is P(ABC) P ( A & B &C ) ? Present your answer in an irreducible fraction.
Suppose A,B, and C are events such that: P(A)=P(B)=P(C)=0.3, P ( A ) = P...
Quiz 1 Probability Rules Name: 1. Suppose that A and B are events for which P(A)-0.3, P(B)-0.5, and P(AB)-0.1. What is the probability that (a) either A or B occurs? (b) A occurs but B does not?
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)?
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
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
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)?
l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3, P[C] = 0.55, P[An B] = For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. (Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint...
S) Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5 What is the probability that (a) either A or B occurs? (b) A occurs and B does not occur? (c) both A and B occur? 4.) A forest contains twenty elk, of which five are captured, tagged and then released. Some time later, four elk are captured from this population. What is the probability that exactly two of these are tagged?...
Consider events A and B such that P(A)=0.3,P(B|A)=0.9,P(B|A¯¯¯)=0.4. Calculate P(A|B¯¯). Give your answer as a fraction in its simplest form.
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)
Given the following: A, B, and C are events. P[A] = 0.3 P[B] = 0.3 P[C] = 0.55 P[A intersect B] = 0 P[A' intersect B' intersect C'] = 0.1 P[A intersect C'] = 0.2 (i) Write a set expression for each of the following events a through d. (ii) Find the probability of the event. (Please show all work. Use venn diagrams if necessary). (a) At least one of the events A, B, or C occurs. (b) Exactly one...