Let A1, A2, ... be a collection of events, not necessarily disjoint. Show that P(A1 N A2 n..) 21– P(A§) – P(A5) – -.. .. Hint: use the theorem about SUBADDITIVITY. You are only allowed to use any fact/formula covered in the

Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…

A: We use the conditional probability formula to prove that A and B are independent.…

Q: A card is drawn from a deck of cards. Events E1, E2, are defined as follows: E1: Getting a face card…

A: Given that E1: Getting a face card E2: Getting an ace card Are E1 and E2 mutually exclusive ?

Q: Suppose that in a certain town with a population of 5000 households, 3000 of the households have…

A: Given that, Suppose that in a certain town with a population of 5000 households, 3000 of the…

Q: Consider four independent events A1, A2, A3, and A4, andlet pi 5 P(Ai) for i 5 1,2,3,4. Express the…

A: Let pi be the probability of the event Ai. Denote qi=1- pi as the probability that event Ai does not…

Q: Let A and B be events with P(A) = 3/10, P(B) = 4/10), and P(AUB) = 6/10. (a) Compute P(AC). (b)…

A: From the provided information, P(A) = 3/10, P(B) = 4/10, and P(A U B) = 6/10

Q: If E and F are events in a probability space with IP(E) + 0, P(F) 7 0, and P(E|F) = P(F|E) then E…

A: We want to tell you above statement is true or false

Q: 5. Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red.…

A: 19 marbles are green, 25 marbles are blue and 6 are red. Hence, total number of marbles in the bag =…

Q: If E and F are events in a probability space with P(E) + 0, P(F)+ 0, and P(EF) = P(F|E) then E and F…

A: The given statement is false here. We find a counter example to prove that statement is false here.

Q: 5. Let A,. A. A, be three independent events. Prove or disprove that Af. Aş, and A are independent.

A:

Q: let A and B be two events in an outcome space M such that M = A U B, P (A) = 0.65 and P (B) = 0.75.…

A:

Q: Let A and B be events in a sample space S2. Prove, from the Kolmogorov Axioms, that PLAAB) = P(A U…

A: Given information: Given that the two events of the sample space are A and B.

Q: b) Let A be the event that a family has children of both sexes and B be the event that a family has…

A: According to given conditions: A= Event representing that a family has children of both sexes. B=…

Q: A1,A2, and A3 are mutually exclusive and exhaustive events such that P(A1) = 0.2,P(A2) = 0.5, and…

A: a)The required probability is calculated as follows.

Q: Let A and B be events with P(A) = 0.8, P (B) = 0.4, and P (B|A) = 0.2. Fins P(A and B).

A: There are two events A and B given with probabilities such as PA=0.8, PB=0.4, and PB|A=0.2.

Q: 3.7 Florin Frenti operates a small, used car lot that has three Mercedes (M, M, M,) and two Toyotas…

A:

Q: Page 2 of 9 1. Suppose A, B, and C are independent events in some proability space, and that P(A) =…

A: It is given that P(A) =0.3, P(B)=0.4 and P(C)=0.5.

Q: mong cats, 2% have a kidney disease . Of tests done, 82% can detect the disease when it is there,…

A: P(D') = 1- P(D) ___________________________________ I am using Bayes' theorem(Also provided Tree…

Q: If A, B, and C are any three events then O a PAUBUC)= P(A) + (B) + P(C)-PANBNC) O b.…

A:

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A: As per guideline expert have to answer first three subparts only.

Q: a) Two events, M and N, are such that P(M) = 0.6, P(M NN) = 0.2, P(M UN) = 0.85 Find P(N \M) State,…

A:

Q: In an audio and video device repair shop, let A be the event in which the component being repaired…

A:

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A:

Q: 13. If {Bk} are events such that >P(Bk) > n – 1, k=1 then P Bx) > 0. k=1

A:

Q: (b) Let E and E, be events with IP(E,) > 0 and P(E2) > 0. Prove that if P(E E2)> P(E1) then P(E2|E1)…

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: Are events A and B mutually exclusive as defined in class? In a single selection: A = Pick a 10…

A: Given In a single selection: A = Pick a 10 of Spades from a deck of cards;  B = Pick a card with a…

Q: Show that if A and Bn (n = 1, 2, 3, ...) are events, then An (U Bn) = U1(AN Bn) 'n=1 'n=1

A:

Q: Let N = {1,2,3, 4, 5, 6}, A = {1,2,3}.Define P(A) = .How far can it extend this probabilistic…

A:

Q: f A and B are events with P(A)=0.6, P(AorB)=0.98, P(AandB)=0.02, findP(B)

A: It is given that P(A)=0.6, P(A or B)=0.98 and P(A and B) =0.02.

Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…

A:

Q: Which of the following statements is false? O Two complementary events cannot occur at the same…

A: complementary events are those events  where only two possible outcomes are there.   Independent…

Q: a) Two events, M and N, are such that P(M) = 0.6, P(M nN) = 0.2, P(M UN) = 0.85 Find P(N |M) State,…

A:

Q: Given that 5% of the Philippine population are female and 15% are older than age 65, can we conclude…

A: Given that 52% of the Philippine population are female. Female  = 52% = 0.52 People older then 65 =…

Q: Suppose E, F1, F2 and F3 are events from a sample space S. a) If p(F1)+p(F2 )+p(F3)> 1, is it…

A:

Q: Prove that if A and B are events, then Pr[An B] > Pr[A] + Pr[B] – 1.

A:

Q: 1. Suppose A and B are two independent events, so by definition P(A N B) = P(A)P(B). a. Prove that A…

A: a) Given A and B are independent events P(A ∩ B) = P(A)*P(B) Venn diagram for A∩BC is shown below…

Q: 2. Let 0 0, P(B| A) = P(B|A), then that event A and B are independent. prove

A: We need to prove, P(AnB) = P(A)P(B)

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any question so I am solving…

Q: Let E, and E, be events with IP(E1) > 0 and P(E2) > 0. Prove that if P(E, E2) > P(E1) then P(E2|E1)…

A:

Q: Let E1 and E2 be events with P(E1)>0 and P(E2)>0. Prove that if P(E1|E2)>P(E1) then P(E2|E1)>P(E2)

A:

Q: Theorem 3-8. For n events A1, A2, ..., A„ 11 P( 4)> U A; 2 E P (A;) – E P (A;^ A) i = 1 i = 1…

A:

Q: nt A: Randomly select a male biology major. nt B: Randomly select a biology major who is 19 years…

A: Mutually exclusive events are events that cannot happen at same time.

Q: Prove the following theorem: If A and B are independent, then so are the following pairs of events:…

A: Given, A and B are independent event i.e. Now, Therefore, A and Bc are independent

Q: 1. Let A and B be random events. Show that if AC B then P(A)<P(B).

A:

Q: Theorem 3-20. If A, B and C are randoni events in a sanple space and if A, B and Care pairwise…

A:

Q: If A is an arbitrary event, then show that P(A) = 1- P(A).

A: Answer: For the given data,

Q: electrical corporation had 2,139,560 electricity customers. Of these, 87% were in the residential…

A: Random experiments are those experiment whose outcomes can not be predicted with any certainty or…

Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P (A U B)

A: Given ,PA=13 , PB=14We know that PA∪B≥PB                    PA∪B≥PA              and PA∪B≤PA+PB

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A:

Q: 29. For any three events A, B and C, show that (i) (ii)

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Prove that if E1, E2,.., En are independent events, then P(E, U E2 U .. U En) = 1- | 1– P(E;)] i=1

A: Given that, E1, E2, ........., En are independent events. We need to prove that: P(E1∪E2 ∪…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.