3. The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table below: On 0.49 Medium 0.11 0.08 ff 0.24 Low 0.05 High 0.03 Consider the following events: A: {Low} B : {Low or On} C: {Off and Medium} D: {High} Complete parts (a) through (h): (a) P(A) = (b) P(B) = (c) P(C) = (d) P(D) = (c) P(A*) = (f) P(AUB) = (8) P(ANC) = (h) Consider each pair of events (A and B, A and C, A and D, B and C, B and D, and C and D). List the pairs that are mutually exclusive.

Q: One thousand randomly selected adults were asked if they think they are financially better off than…

A: Given information: A random sample of n = 1000 people is considered. A two-way classification of the…

Q: Q. 3 If A and B are two events associated with an experiment and P(A) = P(AUB) = and P(AN B) = Find…

A:

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: Find P(B“).

A:

Q: Given P(A and B) = 0.94, P(A) = 0.98, and P(B) = 0.96 are events A and B independent or dependent?

A: Here Given  P(A)=0.98 P(B)=0.96 P(A and B)=0.94

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: Suppose A and B are events in a sample space with P(A) = 0.6, P(B) = 0.65, P(BUA) = 0.84 Find the…

A:

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: Given P(A and B) = 0.07, P(A) = 0.75, and P(B) = 0.63 are events A and B independent or dependent?…

A:

Q: The sample space for an experiment contains five sample points. The probabilities of the sample…

A:

Q: Consider two events with P(B)= .4 and P(A or B)= .9 and P(A and B)= .2  Find P(notA).

A: GivenP(B)=0.4P(A∪B)=0.9P(A∩B)=0.2

Q: In a certain school, the probabilities of the number of students who are reported tardy are shown in…

A: Given :  The probability distribution is  Number tardy: 0 1 2 3 4 Probability: 0.14 0.22 0.37…

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: The sample space for an experiment contains 4 outcomes (1,2,3,4) with probabilities shown below:…

A: Given:  The sample space for an experiment contains 4 outcomes (1,2,3,4) with probabilities shown…

Q: If A and B are two mutually exclusive events with P(A) = 0.6 and P(B) = 0.2, find the following…

A: Given that  P(A)=0.6 , P(B)=0.2 Events A and B are mutually exclusive events  Note: According to…

Q: 16. If P(A) = .30, P(B)= .60, and P(ANB)=D.18, then events A and B are A. dependent B. independent…

A: Here,   P(A) = 0.3 , P(B) =0.60   & P(A∩B) = 0.18     For any two independent events A & B,…

Q: A,B and c are events: P(A)=.35, P(B)=.45, P(C)=.55. Which of these events, if any could be…

A: The probability of event A (say) and the probability of its compliment is equal to 1.

Q: If A and B are independent events with P(A) = 0.5 and P(A ∩ B) = 0.12, then, P(B) = Question 27…

A:

Q: Suppose A and B are events in a sample space with P(A) = 0.61, P(B) = 0.66, P(BUA) = 0.93 Find the…

A:

Q: A film student wanted to investigate the relationship between gender and movie preference. A random…

A: Required probability is P(female AND prefers comedy)

Q: The sample space for an experiment contains 4 outcomes (1,2,3,4) with probabilities shown below:…

A: We have given that,  The sample space for an experiment contains 4 outcomes (S) = (1,2,3,4 )  Ans…

Q: Q. 2 If A and B are two events associated with an experiment and P(A) = p. Find the choice of p for…

A:

Q: Given P(A) = 0.141, P(B) = 0.130, and P(C) = 0.057, and that events A, B, and C are mutually…

A: P(A) = 0.141 P(B) = 0.130 P(C) = 0.057 Events A, B, and C are mutually exclusive i.e.…

Q: b) Let A and B are two events such that: P(A) 0.5, P(B) 0.7, and P(AC n BC) = 0.2, use a Venn…

A:

Q: If two events are independent with P(A) = 0.6 and P (B ) = 0.35 Is A and B are complementary events…

A: Given: P(A)=0.6 P(B)=0.35

Q: Suppose that A and B are two events for which P(A)=0.17, P(B)=0.71, and P(B|A)=0.39 Find each of the…

A:

Q: d B are independent events, P(A)=0.18, and P(B)=0.80, what is P(B|A)?

A: If the probability of occurrence of one event is not affected by the probability of occurrence of…

Q: Given P(A) = 0.28, P(B) = 0.98 , and P(AorB) = 0.47 are events A and B mutually exclusive?

A: Given,

Q: 2. If P(A) = 0.8, P(B) = 0.5, P(AUB) = 0.9, are events A and B independent events? Why or why not?…

A: P (A) = 0.8P (B) = 0.5P(A U B) = 0.9We need to find whether A and B are independent events.

Q: Given P(A) = 0.34, P(B) = 0.60 , and P(AorB) = 0.24 , are events A and B mutually exclusive?

A: Let A and B are two events The given probabilities are, P(A) = 0.34, P(B) = 0.60 ,  P(A or B) = 0.24…

Q: Given P(A) = 0.076, P(B) = 0.184, and P(C) = 0.159, and that events A, B, and C are mutually…

A: Solution: Mutually exclusive events: Two events A, B and C are said to be mutually exclusive when…

Q: If A and B are independent events, P(A)=0.22, and P(B)=0.28, what is P(B|A)?

A: Introduction: Suppose X and Y are two events, with respective probabilities P (X) and P (Y). Denote…

Q: Table 3.1 describes the distribution of a random sample S of 100 individuals, organized by gender…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: If A and B are independent events, and P(A) = 0.2, P(B) = 0.3, find the following:  a)         P(A…

A: Given Data: The probability of event A is: P(A)=0.2 The probability of event B is: P(B)=0.3   Event…

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.