Events U and V are mutually exclusive. P(U) = 0.52 P(V) = 0.16 (a) Find P(U and V) (b) Find P(U or V)

Q: Find: (a) P(R3 I Q)  (b) P(R1' I Q)

A: It is given that P(R1) = 0.15, P(R2) = 0.55, P(R3)= 0.30, P(Q I R1) = 0.40, P(Q I R2)= 0.20, P(Q I…

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Q: P(A) = P (B) = P(AN B)then %3D P[(AN B) U (AN B)] = 1

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Q: II. Proving Show that P(AB) ≥1-P(A)-P(B), where A, B is any two events.

A: A and B two events are given

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Q: Suppose that P(A) = 0.1, P(B) = 0.8 and P(A U B) = 0.3, then P(AnB) = 0.76 O 0.6 O 0.7 None of these

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A: d) We have to find P(N and W),P(M and W) e)P(N or M)=? We have to check whether events N and M…

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Q: If P(A) = 0.7, P(B) = 0.4 and P(A/B) = 0.28, then P(B/A) is %3D %3D Select one: a. 0.16 O b.0.48 c.…

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Q: J and K are independent events. P(J | K) = 0.76. Find P(J) P(J) =

A: Solution: Independent events: Two events A and B are said to be independent if the happening of one…

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Q: Events A and B are independent, where P(A) = 0.25 and P(B) = 0.10. Determine P(A∩B).

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Q: the value of p(1) =0 ulan O

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Q: P(A) = 0.25, P(B) = 0.65, P(AU B)= 0.8 Find a) P(A|B)        b) P(B|A)

A: First we need to find P(AnB). P(AnB) = P(A)+P(B)-P(AUB) = 0.25+0.65-0.8 = 0.1

Q: Use Bayes'Theorem to determine P(B|D) P(B|D)= (Round to two decimal places as needed)

A: Given,   Event A Event B Total Event C 2 5 7 Event D 3 8 11 Event E 17 15 32 Total 22 28…

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Q: Determine P(T < 0.75) Evaluate the E(3T - 4) Find the mean of T. Evaluate E (T²)

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

Q: G and H are mutually exclusive P(G) = 0.5 and P(H) = 0.3 Find P(H or G)

A: Given, P(G)=0.5P(H)=0.3

Q: Given P(A) = 0.22, P(B) = 0.24, and P(B|A) = 0.21, are A and B independent or dependent?

A: We know,  P(B/A) = P(A∩B)/P(A)     P(A∩B) = P(A) P(B) Events A and B are independent if the equation…

Q: onsider the following. P(A) = 0.31 and P(B) = 0.36, and P(A and B) = 0.15 (a) What is P(A | B)?…

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Q: Prove that there is no permutation a such that al(12) a = (34) (15).

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Q: In an election, 70% of the voters were Republicans, and 30% were not. Of the Republicans, 60% voted…

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Q: Q3/ The value of k such that P2 (1) = 2.8, 2 |k 4 f 1 2 Is

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Q: J and K are independent events. P(J | K) = 0.93. Find P(J) P(J) =

A: A and B are the Independent Event if P(A ∩ B) = P(A) P(B)

Q: J and K are independent events. P(J | K) = 0.6. Find P(J). %3D

A: Two events A and B are said to be independent, if P(A|B) = P(A).

Q: Events A and B are such that P(A)=0.70, P(B)=0.40, and P(AUB)=0.90. Find P(B| A).

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Q: U and V are mutually exclusive events. P(U)=0.55 ; P(V)=0.32 Find P(U AND V) =

A: Two events are said to be mutually exclusive events, if two events can not occur simultaneously.

Q: Given P(A) = 0.27, P(B) = 0.27, and P(B|A) = 0.21, are A and B independent or dependent?

A: Events A and B are said to be independent if P(A∩B)=P(A)·P(B) Given:  P(A) = 0.27, P(B) = 0.27, and…

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A: Consider the equation

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.