3. (2 poi ints) Let A and B be independent two events in a sample space....
2. Let C and D be two events exhaustively defining a sample space, we know that P(C) = 0.3, P(D) = 0.4, and P(c n D) = 0.2. what is P(C" n D)?
Problem #3: Let A and B be two events on the sample space S. Then show that a. P(B) P(AOB)+P(AnB) b. If Bc A, then show that P(A)2 P(B) Show that P(A| B)=1-P(A|B) C. P(A) d. If A and B are mutually exclusive events then show that P(A| AUB) = PA)+P(B) Problem 4: If A and B are independent events then show that A and B are independent. If A and B are independent then show that A and B...
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
Let E and F be two events of an experiment with sample space S. Suppose P(E)= 0.4, P(F)=0.3, P(E U F) =0.5, Find P(F|E) and determine if the two events are independent. A) P(F|E)= 3/4, E and F are independent. B) P(F|E)= 3/4, E and F are not independent. C) P(F|E)=1/2 , E and F are independent. D) P(F|E)= 1/2, E and F are not independent.
Question 13 Let A and B be two independent events such that P(A) = 0.2 and P(B) -0.6. Type numbers in the boxes, What is P(A and B)? 10 points Your answer should be given to 2 decimal places.
Let the sample space for an experiment be {1, 2, 3, 5, 8, 13, 21}. Assume you pull one number at random from the sample space. Let A be the event the number pulled is odd Let B be the event the number pulled is greater than 7 What is the probability of event A occurring. What is the probability of B not occuring? What is the probability of A and B occuring? What is the probability of A or...
C3. Let A and B be events associated with sample space S. Using the axioms of probability and possibly the consequences of them to show that P(AUB) P(A) +P(B).
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B) = 0.5 and P(A∩B) = 0.3. Express each of the following events in set notation and find the probability of each event: a) A or B occurs b) A occurs but B does not occur c) At most one of these events occurs