If two events, A and B, are independent then which of the following does not have to be true? (1) P(A)= P(A|B) (2) P(A and B) = P(A)·P(B) (3) P(A)+ P(B)=1 P(A and B) P(A) (4) P(B) =

Q: If events A and B are independent, P(B)-05 and P(A-B)-03, then P(B-A)-

A: The following information has been provided: PB=0.5 PA-B=0.3 We have given that A and B are…

Q: Which pairs of events are independent?     (a) P(A) = 0.67, P(B) = 0.58, P(A∩B) = 0.35.         A…

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Q: P(A)=0.56,P(B)=0.54,P(B∪A)=0.91P(A)=0.56,P(B)=0.54,P(B∪A)=0.91 Find the following probabilities.…

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Q: If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent. true or false?

A: Solution-: If P(A) >0, P(B)>0 and  P(A∩B)=0, then the events A and B are independent. We find…

Q: Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 64. Determine (i) P (? ∩…

A: A and B are two events. The known values are PA=0.64, PB=0.72 and PA∪B=0.86 i)…

Q: When 2 events (A,B) are independent, what is the probability of their union? a.) P(A) + P(B) b.)…

A: Let us consider two events A and B.   Consider A and B are independent events.

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: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

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

Q: For each set of probabilities, determine whether the events A and B are independent or dependent.…

A: We have to find whether events A and B are independent or dependent in each part. Concept/Formula…

Q: If P(A)=0.2, P(B)=0.1, and P(A∪B)=0.3, then P(A∩B)= Are events A and B independent? Are A and B…

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Q: If � ( A ) = 0.24 P(A)=0.24, � ( B ) = 0.52 P(B)=0.52, and � ( A and B ) = 0.12 P(A and B)=0.12,…

A: From the provided information, P (A) = 0.24 P (B) = 0.52 P (A and B) = 0.12

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: (a) Pr(B|A) = 1/2. (b) Pr(B) = 4/7. (c) Pr(A| B) = 7/13. (d) The events A and B are mutually…

A: Given that, A bag contains 4 green balls and 3 red balls. A ball is selected at random from the bag.…

Q: If P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2, then (a)   P(E)= (b)   P(F)= (c)   P(E∪F)= (d) Are the…

A: Given information: P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2. (a)  PF|E=PE∩FPE      0.2  =0.035PE…

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: Q2. Two events A and B are said to be dependent if and only if:

A: Here use basic of dependent events

Q: If three events A, B and C are independent then P(ANBNC) = P(A) x P(B) x P(C) O True False

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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: 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: Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P…

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Q: you are givin the information that P(A) = 30 and P(B) = 0.40. Do you have enough information to…

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Q: ts, A, B, are independent if and only if at least one of the following holds: i) P(A|B) = P(A) or…

A: (e) is correct. It is given that "two events A,B are independent if and only if at least one of the…

Q: P(A)=0.64,P(B)=0.45,P(B∪A)=0.92 Find the following probabilities. P(A∩B) =  P(B|A¯) =  P(A¯|B) =

A: We have given that,  P(A)=0.64, P(B)=0.45, P(B∪A) or P(AUB) =0.92 Then,  We will find the following…

Q: Given P(A) = 0.32, P(B) = 0.44, and the fact that events A and B are independent, What is P(A and…

A: Solution: From the given information, P (A) = 0.32, P (B) = 0.44.

Q: If P(A) = 0.3, P(B) = 0.5, and P(AUB) = 0.74, then P(A^B) = (a) Are events A and B independent?…

A: P(A) = 0.3, P(B) = 0.5, P(A∪B) = 0.74

Q: If P(A) = 0.4, P(B) = 0.9, \ and P(An B) = 0.3, \ then (a) P(A|B) = \ and (b) P(B|A) =

A: We have to find given probability...

Q: (iii)It P(AB) = 0, then the two events A and B are said to be (a) dependent (b) independent (c)…

A: ⇒ P(A∩B) can be written as P(AB).

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 events such that ​P(A)=0.2 and ​P(A∪​B)=0.4​, find​ P(B) when ​(a) A and B are…

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Q: 3 b. X and Y are two events, P(Y)==, P(X|Y)=, and PYoX 10 %3D %3D Find P(XnY) and P(X).

A: Given P(Y) = 35, P(X/Y) = 23     and   PY ∩ X = 310

Q: If P(E∩F)=0.09, P(E|F)=0.45P, and P(F|E)=0.5, then (a)   P(E)= (b)   P(F)= (c)   P(E∪F)= (d) Are the…

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

Q: If two events A and B with P(A) = 0.51, P(B) = 0.28 and P(A or B) = 0.79 then, A and B are

A: GivenP(A)=0.51P(B)=0.28P(A or B)=0.79

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: For two events A and B, P(A)=0.24, P(B)=0.57, and P(A∩B)=0.32. a.Find P(A|B) b. Find P(B|A) c.…

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Q: For each set of probabilities, determine whether the events A and B are independent or dependent.…

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Q: For two events A and B, P(A) = 0.3 and P(B) = 0.4. (a) If A and B are independent, then P(ANB) =…

A: The question is about probability.Given :P ( A ) = 0.3P ( B ) = 0.4

Q: If ​P(A∪​B)=0.6​, ​P(A)=0.4​, and ​P(A∩​B)=0.25​, find​ P(B). Assume that A and B are events.…

A: GivenA and B are eventsP(A∪B)=0.6P(A)=0.4P(A∩B)=0.25

Q: Show that if A and Ą are two events, then P(A) + P(A₂) −1≤ P(Ą_Ą).

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Q: For two events A and B, P(A) = 0.6 and P(B) = 0.3. (a) If A and B are independent, then P(A|B) = P(A…

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.