Q. 2 Two dice are thrown. The events A and B are taken to be Event A - "odd face on first die" Event B - "odd face on second die" Find the following probabilities: P(A) P(A|B) Р(В) | Р(ВА) Are events A and B statistically independent?

Q: Suppose A and B are events in a sample space with P(A) = 0.62, P(B) = 0.67, P(BU A) = 0.91 Find the…

A: Given A and B events of a sample space where; P(A)=0.62P(B)=0.67P(B∪A)=0.91 (a) We know by addition…

Q: A and B are two events such that P(A)-0.5 and P(B)-0.6 and P (AIB) = - then P (AIB) = 0.9 1 0.6 not…

A:

Q: A random experiment has the four outcomes {a,b,c,d) with probabilities p(a)=0.2, p(b)=0.3 and…

A: Given that: Four outcomes of an experiment = {a,b,c,d}  Probability of each outcome:…

Q: Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AN B) = 0.1. Calculate (a) P(A|B); (b)…

A: As per our guidelines we are suppose to answer three sub parts . Given,P(A)=0.5 , P(B)=0.3 ,…

Q: Events A andB are independent. Find the missing probability. P(A) = (2/3), P(B) = (4/5), P(A and B)…

A: We have given that,  A and B are two independent events with    P(A)=(2/3) , P(B) = (4/5)  Then,  We…

Q: Two events A and B have the following probabilities: P (A) = 1/2, P (B)= 3/8, and P(ΑB) - 1/4. Find…

A: For the first question option(C) nominal is correct answer because Nominal data :- It is a…

Q: Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.6, and P(A  B) = 0.15.…

A:

Q: Two events, A and B, are said to be independent if: a. Р(BA) 3D Р(А) b. РАВ) — Р(В) c. P(An B) = PA)…

A: Condition for independence: If A and B are two events, then P(A and B)=P(A)*P(B). Consider option a)…

Q: If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(AnB)=

A: A and B are independent events  P(A) = 0.4  P(B) = 0.6

Q: If two events, A and B, are such that P(A) = 1/6, P(B) = 1/9, and P(An B) = 1/70, find the following…

A:

Q: If A and B are events with P(A)=0.6, P(A OR B)=0.98, P(A AND B)=0.02, find P(B).

A:

Q: When two events A and B are not mutually exclusive, the probability that A or B occur is P(A or B) =…

A: Solution: From the given information, two events A and B are not mutually exclusive.

Q: Two events A and B have the following probabilities: P (A) = 1/2, P (B)= 3/8, and P (A N B) = 1/4.…

A: For events A and B, it is given that, P(A) = 1/2, P(B) = 3/8, and P(A ∩ B) = 1/4.

Q: Let A and B be two events with probabilities P(A) = 0.6, P(B) = 0.4 and P(A and B) = 0.2. (a) Find…

A: Given:  P(A) = 0.6 P(B) = 0.4 P(A and B) = 0.2 Plug in all the given values in the above formula.

Q: 1. Write the expression for each symbolic form. Let p: The children are at school. q: It is a not…

A: Introduction: The expressions for two symbolic forms are given.

Q: The probabilities of events A, B, and AnB are given. Find (a) P(A UB), (b) the odds in favor of and…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If a class has 8 freshmen, 5 sophomores, 4 juniors, and 2 seniors, what is the probabilitythat three…

A: Given: 8 freshmen 5 sophomores 4 juniors 2 seniors Total = 8+5+4+2=19

Q: Two events, A and B, are such that P(A) = 0.08, P(B) = 0.07 and P(B|A) = 0.25. (i) Find P(B), P(A n…

A:

Q: Suppose that A and B are two independent events for which P(A) = 0.17 and P(B) = 0.59 Find each of…

A: For the given data Find p(A/B ) =? P(B/A) =? P( A and B ) =? P (A or B ) =?

Q: Suppose that P(A) - 0.3 and P(B) = 0.6. If events A and B are mutually exclusive, find the following…

A: Mutually exclusive events [MEE]:

Q: Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually…

A: Note : according to our guidelines we can answer only d subpart Given three events, A, B, and C,…

Q: A random experiment has the four outcomes {a,b,c,d) with probabilities p(a)=0.2, p(b)=0.3 and…

A: Answer is 1 1. 0.4 2. 0.5 3. 0.8 4. 0.5 5. 1  6. 0.3

Q: The following two-way table shows the distribution of daily traffic and weather issues in a certain…

A: Given :

Q: P(E:) = 25, P (E>) = 1 An experiment results in one of five sample points with probabilities P P(E)…

A:

Q: Let a&b be events with p(a)=0.2,p(b)=0.8, & p(b/a)=0.3. Find p(a&b)

A: Given Information: A and B are two events. P(A) = 0.2, P(B) = 0.8, P(B|A) = 0.3 To find the…

Q: Let A and B be events with P(A)=.07, P(b)=.44, and P(B|A)=8 P(A and B)= ?

A: Given problem  Given that A and B be events P(A) = 0.07 P(b) = 0.44 P(B|A) = 8 We have to find P(A…

Q: Let A and B be two events with probabilities P(A) = 0.6, P(B) = 0.4 and P(A and B) = 0.2. (a) Find…

A: Given: P(A) = 0.6 P(B) = 0.4 P(A and B) = 0.2 Plug in all the values in the formula.

Q: The following table is based on information from the U.S. Census Bureau regarding the type of health…

A: HealthInsuranceCoverage<18(A)18-44(B)45-64(C)>64(D)TotalPrivate…

Q: Two events A and B have the following probabilities: P (A) = 0.4, P (B)= 0.5, and %3D P (A and B) =…

A: Given that P(A) = 0.4, P(B) = 0.5 and P(A and B) = 0.3

Q: A and C are two events with probabilities, P(A) = 0.34, P(C) = 0.41, P(A | C) = 0.23…

A: Answer: From the given data, P(A) = 0.34 P(C) = 0.41 P(A | C) = 0.23

Q: Let A and B be events with P(A) = 0.6, P(B) = 0.3, and P(A∩B) = 0.2. What is the probability of…

A: The objective of the question is to find the conditional probability of event A given that event B…

Q: When two events are independent, the probability of both occurring is P(A and B) = O P(A) + P(B) O…

A: We have to find correct answer...

Q: Suppose that E and F are two events and that P(E)=0.8 and P(F|E)=0.5. What is P(E and F)​?

A: Given data,  P(E)=0.8  P(F|E)=0.5 P(E and F)​=?

Q: Two events A and B have the following probabilities: P (A) = 0.4, P (B)= 0.5, and P (A and B) =…

A: According to the given information, we have Let A and B be two events, P(A) = 0.4 P(B) = 0.5 P(A and…

Q: If A and B are independant events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

A: It is given that A and B are independent. P(A) = 0.295, P(B) = 0.32

Q: Suppose A and B are two events with probabilities: P(A*) = .25, P(B) = .35, P(A N B) = .30. a) What…

A: Given, P(Ac) = 0.25 => P(A) = 1 - P(Ac)  = 1 - 0.25 = 0.75 P(B) = 0.35 P(A ∩ B) = 0.30

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.