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

Q: Suppose that A, B are two events such that P(A)  = 0.7, P (B) = 0.55 and P  (A / B) = 0.6 Find P (A…

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Q: Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A&B).

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Q: Suppose A and B are events with P(A) = 0.3, P(B) = 0.85, and P(B|A) = 0.6. Find the value of P(A or…

A: given data  P(A) = 0.3 P(B) = 0.85 P(B|A) = 0.6 P(A or B) = ?

Q: Suppose P(E) = 0.3, P(F) = 0.5, and P(E or F) = 0.7. Are the events E and F are mutually exclusive?…

A: It is given that P(E) = 0.3 and P(F) = 0.5.P(E) + P(F) = 0.3+0.5 = 0.8.

Q: If A and B are two independent events, then P(A|B) = P(B) True or false?

A: We have given that,  If A and B are two independent events, then P(A|B) = P(B) True or false?

Q: Suppose that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. Find P(A&B).

A: The Special Multiplication Rule (for two independent event)

Q: Suppose that A and B are independent events with: P(A)= 0.4 P(B)= 0.7 Calculate: P( A U B)

A: The union probability for any two events A and B is defined as P(A ∪ B) = P(A)  + P(B) – P(A ∩ B).

Q: If A and B are independent events, P(A)=0.25, and P(B)=0.79, what is P(B|A)?

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Q: Suppose that A and B are events such that P(A) = 0.84,P(B) = 0.46, and P(A&B) = 0.38. Determine…

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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: Suppose that A and B are mutually exclusive events such that P(A) = 0.25 and P(B) = 0.40. Determine…

A: Special Addition Rule:

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

Q: Suppose A and B are two independent events with P(a)=0.5 and P(b)=0.4 what is the P(A U B)?

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Q: If A and B are independent events, P(A)=0.22, and P(B)=0.71, what is P(B|A)?

A: Given: A and B are independent P(A)=0.22 P(B)=0.71   A and B are independent means that occurring of…

Q: Let A and B be events with P(A) = 0.8 and P(A ∩ B) = 0.2. For what value of P(B) will A and B be…

A: Given,  P(A) = 0.8  P(A ∩ B) = 0.2 P(B)=?

Q: If A and B are independent events with P(A)=0.1 and P(B)=0.7, find P(A AND B).

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

Q: Suppose A and B are dependent events and P(B | A)=0.4, P(ANB)=0.1, P(B')=0.62. Find P(A U B).

A: Consider that A and B are two dependent events.

Q: I. Find P(C U B). J. Are C and B mutually exclusive events? Show why or why not.

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Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A).

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Q: if a and b are independent events with P9A)=0.4 and P(B)=0.5, then P(A or B)=?

A: If a and b are independent events, thenPA and B=PA∩B=PA.PB=0.4×0.5=0.2

Q: Let A and B be two events such that P(A) = 1/6 While P(A or B) = 1/2. Let P(B) = P. For what values…

A: P(A or B)= P(A)+P(B)-P(A and B) For A and B to be independent P(A and B)=P(A).P(B) Therefore, P(A or…

Q: Suppose that we have two events, A and B, with P(A)=0.60,P(B)=0.70, and P(A∩B)=0.40 a. Find P(A∣B)…

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Q: Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/2 and P(A ∪ B) = 5/6. Find (a) P(A ∩…

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Q: Suppose P(E) = 0.3, P(F) = 0.5, and P(E and F) = 0. Are the events E and F are mutually exclusive?…

A: It is given that P(E) = 0.3, P(F) = 0.5 and P(E and F) = 0.

Q: Suppose that A and B are events for which Р(A| B) — 0.8, Р(В A) — 0.15, and Р(A) — 0.2. P(B) =

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Q: Suppose that A and B are events for which P(A) =0.2, P(B)=0.5, and P(A ∩ B)=0.13 P(B|A)=?

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Q: For this problem, assume that Pr[A∪B]=0.55Pr[A∪B]=0.55 and Pr[A]=0.25Pr[A]=0.25. (1) What is…

A: P(A or B) =0.55 and P(A) =0.25. Events A and B are independent.

Q: If P(A) = 3/4 and P(A and B) = 1/2, where A and B are dependent events, then P(B|A) equals?

A: Solution: From the given information, P(A) = ¾ and P(A and B)=1/2.

Q: If A and B are independent events, P(A)=0.25, and P(B)=0.85, what is P(B|A)?

A: Given that, A and B are independent events. P(A) = 0.25 P(B) = 0.85

Q: If E and F are independent events with P(E) =0.4 and P(E or F) = 0.6,then find P(F).

A: It is given that E and F are independent events. The given probabilities are PE=0.4  and PE or…

Q: Let A and B denote the events that the earthquake magnitude is low and the road debris is moderate.…

A: let, A=Earthquake magnitude is low B=Road debris is moderate

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: Suppose that AA and BB are two independent events for which P(A)=0.18 and P(B)=0.8 . Find each of…

A: Two events A and B are said to be independent if; P(A and B)=P(A)×P(B)

Q: Suppose that E and F are two events and that P(E and F)=0.48, P(F)=0.55, and P(E)=0.5. What is P(F…

A: Suppose that E and F are two events and that P(E and F)= 0.48 P(F)=0.55 and P(E)=0.5 What is P(F |E)…

Q: AA and BB are independent events. If Pr(A∩B)=0.28 and Pr[A]=0.4, what is Pr[B]?

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Q: if two events A and B are manually exclusive, what is the value of P(A and B)?

A: If two events not occur at same time,then those events are called as mutually exclusive events.

Q: Suppose that E and F are two events and that N(E and F)=450 and N(E)=750. What is P(F|E)?

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Q: Suppose that C and D are events such that P(C) = 0.35,P(D) = 0.40, and P(C&D) = 0.30. Determine…

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Q: Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine…

A: Given, P(C) = 0.14  P(D) = 0.32  P(C or D)=?

Q: Suppose A and B are events with P(A) = 0.3, P(B) = 0.65, and P(B|A) = 0.6. Find the value of P(A or…

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Q: For this problem, assume that Pr[A∪B]=0.85 and Pr[A]=0.5Pr[A]=0.5. What is Pr[B] if A and B are…

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Q: If A and B are independent events with P(A)=0.6 and P(B)=0.2, find P(A AND B).

A: P(A) = 0.6 P(B) = 0.2

Q: Suppose that A and B are independent events with P(A) = .40 and P(B) = .70, then P (B'/A') is

A: Given information- P(A) = .40 P(B) = .70 We have to find P (B'/A'). We know that- P(A’) = 1 - P(A)…

Q: Can you explain: P(M^c ) union P(R)= P(M^c) +P(R) I thought this was true for only mutually…

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Q: Suppose A and B are mutually exclusive events, and that P(B)=0.44 and P(A OR B)=0.81. Find P(A).

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Q: If E and F are mutually exclusive events with P(E) = 0.11 and P(F) = 0.38, then the value of P(EUF)…

A: Given that P(E) = 0.11, P(F) = 0.38

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.