In a soon to be released Halloween martial arts movie, a pumpkin has a starring role. Because of the rather violent nature of the film, the producers have also hired a stunt pumpkin.  Suppose the featured pumpkin appears in 40% of all the film scenes, the stunt pumpkin appears in 30% of the film scenes and the two appear simultaneously in 5% of the scenes. Draw the Venn diagram to reflect information given in the problem. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene mutually exclusive (disjoint)? Explain how you know. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene independent? Explain how you know.

Q: Has been loyal I or more years, given that he or she is from the east? Has been loyal I or more…

A: The conditional probability can be obtained as P(A | B) = P(A and B)/P(B) And two events A and B are…

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: Given that P(A) = 0.42, P(B) = 0.04, and P(A and B) = 0.0168, are events A and B independent?

A: It is given that P(A)=0.42, P(B)=0.04, and P(A and B)=0.0168.

Q: Given P(A and B) = 0.16, P(A) = 0.20, and P(B) = 0.80 are events A and B independent or dependent?

A: GivenP(A)=0.20P(B)=0.80P(A∩B)=0.16

Q: Given P(A and B) = 0.94, P(A) = 0.98, and P(B) = 0.96 are events A and B independent or dependent?

A: Here Given  P(A)=0.98 P(B)=0.96 P(A and B)=0.94

Q: Given P(A) = 0.47, P(B) = 0.41, and P(A or B) = 0.88, are events A and B mutually exclusive?…

A: Events A and B are mutually  exclusive when  Hence, Event A and B are mutually exclusive.

Q: If A and B are events with P(A)=0.2, P(A OR B)=0.74, and P(A AND B)=0.06, find P(B).

A:

Q: The following table summarizes the outcome for 70 people who attended a picnic, some of whom ate…

A: From the given information,   Yes No Total Salad-Yes 22 24 46 Salad-No 1 23 24 Total 23 47…

Q: Given P(A and B) = 0.56, P(A) = 0.72, and P(B) = 0.81 are events A and B independent or dependent?

A: Given dataP(A and B) = 0.56, P(A) = 0.72, and P(B) = 0.81For the events to be independentP(A and B)…

Q: Given P(A and B) = 0.42, P(A) = 0.92, and P(B) = 0.05 are events A and B independent or dependent?

A:

Q: If A and B are events with P(A)=0.4, P(A or B)=0.53, and P(A and B)=0.07, find P(B)

A:

Q: If two events, A and B,

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

Q: If the outcome of event A is not affected by event B, then events A and B are said to be* 2.

A: Answer: If the outcome of event A is not affected by event B, then events A and B are said to be…

Q: Show that if events A and B obey the multiplication rule, P(A and B) = P(A) P(B), then A and the…

A: It is given that A and B follows the rule P(A∩B)=P(A)·P(B) that means the events A and B are…

Q: Given P(A) = 0.47, P(B) = 0.41, and P(A or B) = 0.88, are events A and B mutually exclusive?

A: Mutually exclusive events: The two events A and B are mutually exclusive events, then probability P…

Q: A,B and c are events: P(A)=.35, P(B)=.45, P(C)=.55. Which of these events, if any could be…

A: The probability of event A (say) and the probability of its compliment is equal to 1.

Q: Given P(A) = 0.03, P(B) = 0.42, and P(A or B) = 0.11, are events A and B mutually exclusive?

A: Given: P(A) = 0.03 P(B) = 0.42 P(A or B) = 0.11 Objective of the question is to find if A and B are…

Q: Given that P(A) = 0.47, P(B) = 0.07, and P(A and B) = 0.0329, are events A and B independent? O Yes,…

A: No. They are not independent.

Q: Suppose that A,B, and C are three events that cannot all occur simultaneously. Does this condition…

A: Venn diagramVenn diagram is a diagrammatic representation of sets which shows the relationship…

Q: Given P(A) = 0.35, P(B) = 0.08, and P(A or B) = 0.43, are events A and B mutually exclusive?

A: Given: P(A) = 0.35 P(B) = 0.08 and P(A or B) = 0.43

Q: Given P(A) = 0.51, P(B) = 0.79, and P(A or B) = 0.66, are events A and B mutually exclusive?

A:

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,…

A:

Q: Suppose two events E and F are disjoint.  Which of the following is true? A.) P (E or F) = 1 B.) P…

A: If E and F are disjoint then there is no common area between E and F They roughly look like: So the…

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: Suppose two events E and F are disjoint.  Which of the following is true?   (1 answer) A. P(E or F)…

A: If two events E and F are disjoint then P(E and F)=0

Q: Given P(A and B) = 0.94, P(A) = 0.98, and P(B) = 0.96 are events A and B independent or dependent?

A:

Q: Given P(A and B) = 0.20, P(A) = 0.49, and P(B) = 0.41 are events A and B independent or dependent?

A: Let A and B are two events. The known Probabilities are P(A and B) = 0.20, P(A) = 0.49, and P(B) =…

Q: 1. Draw the tree diagram. 2. probability of a successful well in field A, B. probability of a…

A: Here define events  S = successful well in field A = successful drill in field A B = successful…

Q: Given P(A)=0.31, P(B)=0.49 and P(A or B)=0.78, are events A and B mutually exclusive

A: According to the given information, we have P(A) = 0.31 P(B) = 0.49 P(A or B) = 0.78

Q: Consider two events A and B. Use Venn diagram to show that (AU B) \ A = B\ A

A: For any two events A and B. Using venn diagram,  we need to show that: (AUB)\B = B\A

Q: Suppose an event E and its complement E then P(E) +P(E) = 1 P(E) +P(E) =0 P(E) - P(E) =1 P(E) P(E)…

A:

Q: Given the following Venn diagram, create a dependent situation and label each of events as they…

A: Euler Venn Diagram or commonly known as Venn Diagram, is a diagrammatic representation to represent…

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…

A:

Q: The events A and B are such that ?(?) = 4/9?(?|?) = 1/2?(? ∪ ?) = 2/3 (i) Draw a Venn diagram to…

A:

Q: Given P(A) = 0.13, P(B) = 0.02, and P(A or B) = 0.15, are events A and B mutually exclusive?

A: Given that  P(A)=0.13 P(B)=0.02 P(A or B)=0.15 Definition of Mutually Exclusive- Two events are said…

Q: Given P(A and B) = 0.43, P(A) = 0.81, and P(B) = 0.25 are events A and B independent or dependent?

A:

Q: Suppose two events E and F are independent.  Which of the following is true?   (1 answer) A. P(E and…

A: Given that two events E and F are independent.

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

A: we have given that  independent events .

Q: Given P(A) = 0.27, P(B) = 0.19, and P(A or B) = 0.46, are events A and B mutually exclusive

A: Given,  P(A) = 0.27 P(B) = 0.19 P(A or B) = 0.46

Q: Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17. Are A and B…

A: Answer -  Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17.…

Q: Given P(A) = 0.22, P(B) = 0.60, and P(A or B) = 0.82, are events A and B mutually exclusive?

A: Two events A and B are said to be mutually exclusive, if P(A and B) = 0.

Q: For any two events A and B, show that P(ĀOB)=P(B) –- P(A B).

A: Answer: From the given data, A and B are any two events

Q: If A and B are events with P(A)=0.4, P(A OR B)=0.78, and P(A AND B)=0.12, find P(B).

A: Probability: Probability is a chance factor that occurs at every outcome of a random experiment and…

Q: Given P(A) = 0.20, P(B) = 0.30, and P(A or B) = 0.50, are events A and B mutually exclusive?

A: Solution: Mutually exclusive events: Two events A and B are said to be mutually exclusive when the…

Q: Given P(A and B) = 0.34, P(A) = 0.94, and P(B) = 0.36 are events A and B independent or dependent?

A: Given  P(A and B) = 0.34, P(A) = 0.94, and P(B) = 0.36 are events A and B independent By the…

Q: If A and B are events with P(A)=0.5, P(A OR B)=0.75, and P(A AND B)=0.05, find P(B).

A:

Q: events A and B mutually exclusive?

A: Given P(A) = 0.10, P(B) = 0.08, and P(A or B) = 0.18,

Q: Given P(A) = 0.34, P(B) = 0.60, and P(A or B) = 0.24, are events A and B mutually exclusive?

A: We have given that- P(A) = 0.34 P(B) = 0.60 P(A or B) = 0.24 We know that two events are mutually…

Q: Given P(A and B) = 0.12, P(A) = 0.58, and P(B) = 0.44 are events A and B independent or dependent?

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

Q: Given P(A) = 0.02, P(B) = 0.71 , and the fact that events A and B are independent What is P(A and…

A: Probability of event A is P(A)=0.02 Probability of event B is P(B) =0.71.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.