Let A and B event with. P(A)=0.3, P(B)=0.16 Find: • P(An B) If A and B are independent • P(B|A), If i) A and B are independent i) A and B are disjoint

Q: (a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A).

A: As per our guidelines, we are allowed to answer first question only. Thanks   Given Events A and B…

Q: According to special rule of addition P(A or B) = P(A) + P(B), is true if and only if a.A and B are…

A: We need to find the special rule of addition for which P(A or B) = P(A) + P(B) is true .

Q: Let C and D be events such that​ Pr[C] =0.8​, Pr[D] =0.6​,and Pr​ [C ∪​ D] =0.9. Find.. Pr[C |​…

A: Given,     The objective is to find the required probabilities.

Q: Given that P(A) = 0.33, P(B) = 0.16, and P(A and B) = 0.0297, are events A and B independent?

A: Solution: From the given information, P (A) = 0.33, P (B) = 0.16 and P (A and B) = 0.0297.

Q: 1. Let A and B be events such that, P(A) = 0.6, P(B) = 0.7, P(A N B) = 0.4 Find %3D a. P(A U B) b.…

A: Given that, A and B are events, PA=0.6PB=0.7PA∩B=0.4

Q: Consider two events B and C, such that P(B) = 0.28, P(C) = 0.46, and %3D P(C n B) = 0.2, then P(C n…

A:

Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)>0

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 two events such that p(A) = 0.4 and P(BA) = 0.2. Then P(BnA) = 0.4 0.7 0.6 0.5

A:

Q: For two events E and F, P(E) = 0.30, P(F) = 0.40, and P(E U F) = 0.70. Are E and F mutually…

A: Introduction: The occurrences that cannot occur or cannot occur at the same time are said to be…

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: Given that P(A) = 0.13, P(B) = 0.31, and P(A and B) = 0.0052, are events A and B independent? Yes,…

A:

Q: Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]

A:

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: Suppose the events B1 and B2 are mutually exclusive and complementary events, such that P(B1) = 0.75…

A: According to the given information, we have B1 and B2 are two mutually exclusive and complementary…

Q: Let A and B be events with P(A) = 0.7, P(B) = 0.9, and P (A and B) = 0.6. Compute P (A or B) Are A…

A: a.

Q: Given that A and B are independent events, show that ?̅ and B are also independent events

A: Given: Given that A and B are independent events, show that ?̅ and B are also independentevents

Q: For events A and B, prove that P (An B) >1– P (Aº) – P (Bº).

A: We want to prove the above result. Result: 0≤P(A)≤1

Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)

A:

Q: d. Are the events Freshman and Live on Campus mutually exclusive? Why? Choose a number below 1. Yes,…

A: d. P(Freshman∩Live On Campus) =73920467 P(Freshman∩Live On Campus) =0.0361 3. No, since…

Q: Given that P(A) = 0.01, P(B) = 0.11, and P(A and B) = 0.0010, are events A and B independent? %3D…

A: Answer

Q: (c) State an event which is (i) complementary with G; (ii) mutually exclusive with M.

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

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

A: P(A) = 1/3, P(B) = 1/4.

Q: a. What is P(Xi= 1, X2= 1), that is, the probability that there is exactly one customer in each…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   Given :

Q: Suppose that A, B are two independent events, with P(A) = .1 and P(B) = .2. Find P(A|B).

A:

Q: Given that A and B are independent events, show that A and B are also independent events.

A:

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

A:

Q: 7. If two events A and B are mutually exclusive, then P(A N B) = computed from the fomula P(A U B) =…

A: If two events A and B are mutually exclusive, then PA∩B=______. As a result, PA∪B can be computed…

Q: Consider two events B and C, such that P(B) = 0.28, P(C) = 0.46, and P(C n B) = 0.2, then P(C n B)…

A: Given that P(B) = 0.28, P(C) = 0.46, P(C' AND B) = 0.2

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: 2]. Let the events A = {x 0.75}. (a) Find the probabilities of A, B, A N B, and A Nc. (b) Find the…

A: Calculate the events of A,B and C. A=[-1,0) Since, A=x<0. Given that, B=|x-0.5|<0.5 Thus,…

Q: Let A and B be mutually exclusively  events with P(A)=0.24 and P(B)=0.34

A: If A and B are mutually exclusive events then, P(A ∩ B) = 0 Now we know that P(A U B) = P(A) + P(B)…

Q: CONSIDER two events A and B PROVE that if Bc A then P(B) < P(A)

A: We have to answer question based on set

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: Given that A be the event that a family has children of both sexes and B be the event that a family…

Q: A and B are independent events. If Pr[A]=0.3 and Pr[B]=0.7, what is Pr[A∩B′]?

A: From the provided information,

Q: If A and B are mutually exclusive events, then prove that P ( A )<P ( B° )

A:

Q: Let A and B be two events with P(A) = 0.13, P(B) = 0.04 and P(AUB) = 0.1323. %3D %3D Then, A and B…

A: If Two events are Disjoint their intersection will be zero. If two events is independent their…

Q: Let A, B, be two independent events such that P(A) = P(B) = 0.3 then P(A UBC) =

A: Given that PA=PB=0.3 A and B are independent events. Hence, P(A and B)=P(A)*P(B)=0.3*0.3=0.09

Q: If A & B are two events and p(B) ≠ 1, prove that p(A/B') = [p(A) - p(A∩B)/[1 - p(B) where B'…

A: We have, two events A and B thus,  P(A|B')=P(A∩B')P(B')          ......(1)We know that,…

Q: Suppose that C and D are events such that P(C) = 0.5 and P(C&amp;D) = 0.2. Determine P(D| C).

A: Conditional probability is the probability that one event will occur given that another has already…

Q: I toss a fair die twice, and obtain two numbers X and Y. Let A be the event that X=2, B be the event…

A: A fair dice have 6 faces 1, 2, 3, 4, 5 and 6 and let X and Y be the two numbers obtained in a toss.

Q: Suppose A and B are mutually exclusive events such that P(A) = .3 and P(B) = .4. Suppose C is an…

A:

Q: If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B)…

A: Disjoint events : if two events A and B are disjointevents then the two events can not occure at the…

Q: Let A and B be events such that 0

A:

Q: Let A and B be events with P(A) = 0.1 and P(B) = 0.4. Assume that A and B are independent. Find P(A…

A: We have given that,  A and B are two independent events with     P(A) = 0.1 and P(B) = 0.4 Then, We…

Q: Suppose that in a given town, 60% of the population is under age 40 (event A). It is found that the…

A: The independent events are when two events doesn't effect each other. This means that the…

Q: IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also…

A: Answer: For the given data,

Q: For any event A, P (A U Ã) =1 True or false

A: for any event A, A¯  is complement of A. then A¯∩A=∅

Q: Let A and B be events with P(A) = 0.5, P(B)=0.95, and P(B|A) = 0.1. Find P (A and B). P(A and B) =

A: Given that, P(A) = 0.5P(B) = 0.95P(B|A) = 0.1

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.