Is Event B dependent or independent of Event A?   A: A mosquito lands on your arm. B: You get a mosquito bite

Q: are events A and B independent?

A: For the events to be independent, we must have P(A and B) = P(A).P(B)

Q: Are the following events disjoint? 1) Arriving early for your next statistics class. 2) Arriving…

A: Disjoint event are those events that never occur at the same time

Q: Given that P(A) = 0.33, P(B) = 0.16, and P(A and B) = 0.0297, are events A and B independent?

A: Solution: From the given information, P (A) = 0.33, P (B) = 0.16 and P (A and B) = 0.0297.

Q: Suppose a coin is tossed three times. A: Heads on the first toss B: Writing on the second shot C:…

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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 E and F be independent events with P(E) = 0.2 and P(F) = 0.2. What is the probability that at…

A: Solution: From the given information, E and F are independent events, P(E) = 0.2 and P(F)= 0.2.

Q: If P (A) = 0.8, P (B) = 0.5, and P (A∪B) = 0.9, are A and B independent events? Why or why not?

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Q: Let A and B be events. a. Use probability notation to represent the conditional probability that…

A: a. The conditional probability of an event B is the probability that the event will occur given the…

Q: Consider two independent events A and B.Suppose it is known that P(A)=0.27 and P(A or B)=0.5474.…

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Q: 1) Let P(A) = 0.2, P(B) = 0.6 and P(A or B) =0.5. Are events A and B mutually exclusive? Why or why…

A: Thank you for posting the question. Since you have asked multiple question, we will solve the first…

Q: the h iflis isiran'event in

A: Answer can be given using concept of probability.

Q: 13) Suppose that P(A) = 0.4, P(B) = 0.3 and P(AU B) = 0.6, then what is the conditional probability…

A: Given: P (A) = 0.4 P (B) = 0.3 P (A U B) = 0.6 P (B | A) needs to be calculated.

Q: Given P(A) = 0.061, P(B) = 0.197 and P(C) = 0.080 , and that events AB, and Care mutually exclusive,…

A: Given: P(A)=0.061P(B)=0.197P(C)=0.080 Since all three events are mutually exclusive. The objective…

Q: Given that P(A) = 0.06, P(B) = 0.23, and P(A and B) = 0.0258, are events A and B independent? Yes,…

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Q: Answer true or false to the following statement and justify your answer: If event A and event B are…

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Q: Given that events "A" and "B" are independent, P(A) = 0.80, and P(A and B) = 0.24, what is P(B)?

A: If two events A and B are independent, then P(A∩B)=P(A)*P(B) Given, P(A)=0.8 and P(A∩B)=0.24 So, it…

Q: f ?A and ?B are disjoint events (mutually exclusive events) with ?(?)=0.3P(A)=0.3 and…

A: Solution: Let A and B are mutually exclusive events with P(A)= 0.3  and P(B)=0.4

Q: Given P(A and B) = 0.17, P(A) = 0.21, and P(B) = 0.81 are events A and B independent or dependent?…

A: Two events A and B are called independent if  P(A and B)= P(A)*P(B)

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: Is it possible for events A and B to be both mutually exclusive and independent? Justify your…

A: Disjoint Events:  Two events A and B are disjoint or mutually exclusive if and only if both do not…

Q: Given that A and B are independent events, show that A and B are also independent events.

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Q: (i) If a Gauteng resident is selected at random, what is the probability that (a) he is under 21 and…

A: Here AS PER POLICY I SHOULD HAVE TO CALCULATE 3 SUBPART ONLY EVEN THOUGH I HAVE CALCULATED 4 PLZ…

Q: Given the following information about events A B, and C: ​…

A: From the provided information,

Q: Given P(A) = 0.54, P(B) = 0.40, and the fact that events A and B are independent, What is P(A and…

A: P(A) = 0.54 P(B) = 0.40 Event A and Event B are independent events.

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: E. If P(A)=0.8, P(B)=0.5, and P(AUB)=0.9, are A and B independent events? Why or why not

A: P(A) = 0.8 P(B) = 0.5 P(A U B) = 0.9   P(A ∩B) = P(A) + P(B) - P(A ∪B) P(A ∩B) =0.8 + 0.5 - 0.9P(A…

Q: For a medical experiment, people are clas-sified as to whether they smoke, have a family history of…

A: E: person smokes F: person has a family history of heart disease G: person is overweight

Q: Given P(A) = 0.91, P(B) = 0.35, and the fact that events A and B are independent, What is P(A and…

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Q: Given P(A) = 0.08, P(B) = 0.26, and the fact that events A and B are independent,

A: Given P(A) = 0.08, P(B) = 0.26 the fact that events A and B are independent.

Q: b) Given that A and B are independent events, show that A and B are also independent events.

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Q: Answer true or false to the following statement and justify your answer: If event A and event B are…

A: The statement is “If events A and B are not mutually exclusive, neither are events A, B, and C for…

Q: Decide whether the following pairs of events are dependent or independent. A red and a green die are…

A: The given statement is "A red and a green die are rolled. A is the event that the red die comes up…

Q: The statement that “?(?|?) = ?(?|?) whenever ? and ? are independent events” is

A: we have given that  independent events .

Q: 1. Which event is illustrated in the Venn diagram below? A OO P(A or B) A. Dependent Event B. Not…

A: As per our guidelines we can solve first multiple-choice question and rest can be reposted.…

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: Are the events A and B mutually exclusive? d) Are the events A and C disjoint? e) Are the events A…

A: Given that  S = {1,2,3,4,5,6,7,8,9,10}  A = {1,2,3,4,5}, B = {4,5,6,7,8} C= {7,9}.

Q: Determine whether each of the following statements is true or false, and explain why. If two events…

A: Given-  If two events are mutually exclusive, then they are independent. To determine- whether the…

Q: Aeovem 041 AC iS Ahe complemend of an event A, then fLA)= 1- PCA).

A: It a lemma that P(A')= 1-P(A). P(A') is compliment probability of A.

Q: 16. Two coins are tossed. If A is the event “two heads" and B is the event "two tails ". A and B…

A: Two events are said to be mutually exclusive if happening of one event precludes the happening of…

Q: a) Prove the De Morgan's rule for events A and B using Venn diagram

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Q: Given P(A) = 0.67, P(B) = 0.49, and the fact that events A and B are independent, What is P(A and…

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Q: Suppose that events E and F are independent, P(E) = 0.3, and P(F) = 0.9. What is the P(E and F)? The…

A: The union and intersection probabilities of two events A and B are related by the following formula:…

Q: Consider events A and B that are independent. Let P(A) = 0.2 and P(B) = 0.3. What is the probability…

A: Given data P(A) = 0.2 P(B) = 0.3 P(both event occurs) =?

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: Question No.1- Define Events? Differ

A: To define: 1).Events 2).Difference between union and intersection of two events

Q: .  An airline tracks data on the flight arrivals. Over the past 6 months, 65 flights on one route…

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Q: Are the two events "owning a dog" and "owning a cat" complementary? O YES O NO O CAT O DOG

A: We have to find the

Q: AUB is the event that occurs if ..... .A A occurs and B occurs .B A occurs or B occurs (or both)

A: Given : Let A and B be the two event  A∪B : It is the union of A and B It means that occur event A…

Q: Consider events A and B that are independent. Let P(A) = 0.2 and P(B) = 0. probability that both…

A: Events A and B are independent. P(A)=0.2 P(B)=0.1

Q: If A and B are independent events, P(A)=0.28, and P(B)=0.67, what is P(B|A)?

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

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.