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

A:

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: 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: 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 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 independent events, P(A) = 0.45, and P(B) = 0.15, find the probabilities below.…

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).

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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.

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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: 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: 2. Two events A and B are such that P(A)=0.21, P(B) = 0.29, P(A|B)=; 29 Calculate the probabilities…

A: P(A) = 0.21P(B) = 0.29P(A|B) = 829

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 have probabilities .3 and .5 respectively. It is also known that P(A n Bº) = .2.…

A: As per our guidelines we are suppose to answerthree sub parts.Given,P(A)=0.3P(B)=0.5P(A∩Bc)=0.2

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…

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Q: The probabilities of events E, F, and ENF are given below. Find (a) P(E|F), (b) P(FIE), (c) P…

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Q: 4. P4 = P(A | Bº). (P1, P2, P3, P4) =(

A: From the given information we have P(B) = 47/210 P(Bc) = 1 - P(B) = 1 - 47/210 = 163/210

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: Find the probability that there are at least 3 earthquakes in the next 2 month. Let T be the time…

A:

Q: At the corner of Texas Ave and University Dr the probability of vehicles of a particular make and…

A: Part (i):It is given that B, F and K represent models of cars; R represents the colour red. Also, P…

Q: Suppose you roll two dice. Let X represent the number of even numbers appearing on the dice. For…

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

A: 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: Suppose A and B are two events with probabilities: P(A) = .50, P(B) = .40, P(A N B) = .25. a) What…

A: Given P(A)=0.5P(B)=0.4P(A∩B)=0.25 Formula of conditional probability A given B is:P(A/B)=P(A∩B)P(B)…

Q: A 13-sided die is rolled. Find the probability of the given event. (a) The number şhowing is a 11;…

A: From the provided information, A 13-sided die is rolled. Total outcomes = 13 Sample space = {1, 2,…

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: Suppose A and B are two events with probabilities: P(A°) = .40, P(B) = .25, P(A U B) = .75. Find the…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

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: 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

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.