Use the diagram to find the probabilities below. (a)    P(A) (b)    P(E | A) (c)    P(A E)

Q: If A and B are independent events, P(A) = 0.45, and P(B) = 0.45, find the probabilities below.…

A:

Q: What are properties that only, independent events have? Select all. P(AN B) P(B) P(A| B) O P(A| B) =…

A: The two events are said to be independent if occurrence of one event doesn't depend on the…

Q: select the same hand signal, the game results in a tie. Two roommates, roommate A and roommate B,…

A: Given that probability of event A = 0.24. Thus, P(A) = 0.24

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

A: Hello. Since your question has multiple parts, we will solve first 3sub parts question for you. If…

Q: Assume that E and F are two events with positive probabilities. Show that if P(E|F) = P(E), then…

A: Given that E and F are two events with positive probabilities.And Using formulas,

Q: The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is…

A:

Q: 0.2 Find each probability by referring to the tree diagram above. (a) P(C|A) = (b) P(D|B) = (C) P(Αn…

A:

Q: The Venn diagram below shows the 11 students in Ms. Bailey's class. The diagram shows the…

A: Total number of students : n=11 A : Student is in the Music club B : Student is in the Basketball…

Q: Given that P(A)P(A) = 0.4, P(B)P(B) = 0.51, and P(A∣B)P(A∣B) = 0.63, find the probabilities:…

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Q: (a) Find the probabilities of the events below. Write each answer as a single frection. P(4) - P(B)…

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Q: Supposed P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive.  Find: a) P(G)…

A: (a)If events F and G are mutually exclusive, then, P (F or G) = P(F)+ P(G).Or, P(G) = P (F or G) –…

Q: (A) (B) (C) Brand A Brand B Brand C (P) 5. Cup (E) 6 6 8. Cone Select all that apply. Which two…

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Q: 1. In the communication system below the probability of transmitting ("B" before) symbols 1 and are:…

A: From the given information, P(B1)=0.7 P(B0)=0.3 P(A1|B1)=0.8 P(A0|B1)=0.2 P(A0|B0)=0.9 P(A1|B0)=0.1…

Q: Given that P(A)P(A) = 0.49, P(B)P(B) = 0.63, and P(A∣B)P(A∣B) = 0.46, find the probabilities:…

A: As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Q: The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a…

A:

Q: Suppose events B and C are independent and P(B) = 1 P(C) = 1 3 6 Find the probability. (Enter the…

A: Here given that P(B) = 13     P(C) = 16A, B are independent so P(A,B) = P(A).P(B)

Q: We are asked to find the probability of event A occurring given that event B occurs. This is…

A: By conditional probability theorem, the probability of event A occurs, provided that the event B has…

Q: Solve

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Q: (a) Find the probabilities of the events below. Write each answer as a single fraction. P(A) = P (B)…

A: From the given Venn diagram Total students = 8

Q: If A and B are independent events, P(A) = 0.15, and P(B) = 0.55, find the probabilities below.…

A: Sol:- (a) Since A and B are independent events, the probability of both events occurring (i.e., the…

Q: The Venn diagram below shows the 8 students in Ms. Taylor's class. The diagram shows the memberships…

A: Given n=8

Q: P(A and B) =0.43 P(B)=0.8 Find the conditional probability of  A given B?

A: It is given that, P(B)=0.8 P(A and B) =0.43

Q: If A and B are independent events, P(A) = 0.35, and P(B) = 0.35, find the probabilities below.…

A: a)

Q: Determine if events [A] and [B] are independe P(A) - P(B)- 3 P(A and B) 10 3 25 Answer: 1 P(A and B)…

A: if events [A] and [b] are independentP(A and B)=P(A).P(B)

Q: The table gives a set of outcomes and their probabilities. Let  A  be the event "the outcome is a…

A: The objective of the question is to find the probability of event A, which is defined as the event…

Q: (d)    P(E) (e) Does P(A E) = P(A) · P(E)? Yes No     (f) Are A and E independent events? Yes…

A: Using Bayes Theorem this problem can be solved

Q: Given that P(A)P(A) = 0.37, P(B)P(B) = 0.36, and P(A∣B)P(A∣B) = 0.31, find the probabilities:…

A: Given that P(A) = 0.37, P(B) = 0.36, and P(A∣B) = 0.31 find the probabilities:

Q: P(A)= 0.33, P(B)= 0.32, P(A and B) = 0.12 What is the conditional probability A given B? P(A…

A: Answer: From the given data, P(A) = 0.33 P(B) = 0.32 P(A and B) = 0.12

Q: Probability Trey has 12 marbles as shown in the diagram below. Each marble is either blue (labeled…

A: Given that  Total marbles=12 Yellow marbles=3 Red marbles=7 Blue marbles=2

Q: (a) Find the probabilities of the events below. Write each answer as a single fraction. P(A or B) =…

A:

Q: Three boys, Kofi, E 11 target are a 4 3 (i) they all miss,

A: Solution

Q: You and I play the following game: I toss a coin repeatedly. The coin is not necessarily fair and…

A: The provided information is as follows:The given coin is not necessarily fair.The probability of…

Q: When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do…

A: Complementary events:   Let A denote an event defined, and then the complement of the event A is…

Q: Selling a car: A - Event a potential buyer will read the add: P(A) = .3 B - Event an advertisement…

A: Given : Let A be the event that a potential buyer will read the add P(A) = 0.3 Let B be the event an…

Q: a)P(Ā) c)P (A nΒ) (d)P (A n Β)

A: Given P(A) = 0.45 P(B) = 0.3 to find i) P(A) ii) P(A n B) iii) P(A n B)

Q: (a) Find the probability that the person opposed the tax or is female. P(opposed the tax or is…

A: Here the given table isSample size , n = 1062Using formula,

Q: Given that P(A)P(A) = 0.62, P(B)P(B) = 0.27, and P(A∣B)P(A∣B) = 0.22, find the probabilities:…

A:

Q: P(A and B) = 0.18. Find the conditional probability P(A | B)?

A: Given:  P(A) = 0.34 P(B) = 0.36 And P(A and B) = 0.18

Q: Let A and B be events with P(A)=0.4, P(B)=0.3, and P(A and B)=0.02. (a) Are A and B independent?…

A: Answer Given P[A] =0.4P[B] =0.3P [A and B] =0.02

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

A: Given: P(A ∩ B) = 0

Q: Multiplication rule, says that P(A and B) = P(A) x P(B). What must be true about events A and B…

A: Solution -Multiplication rule, says that P(A and B) = P(A) x P(B). What must be true about events A…

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.