There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.3, P(F) = 0.3, and P(En F) = 0.12. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(E U F)? (b) What is the probability that Darlene doesn't have to stop at either light? (c) What is the probability that Darlene must stop at exactly one of the two lights?

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A: Here  Family has 3 children with at least one boy and one girl.

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Q: Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is…

A: Answer:- Let, Event X = "she's up all night 'til the sun" Event Y = "she's up all night for good…

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A:

Q: Let E be the event that a new car requires engine work under warranty and let T be the event that…

A: Probability of car requires engine work under warranty =P(E)=0.05 Probability of car requires…

Q: Suppose that Joe arrives home on time with probability 0.8. If Joe does not arrive home on time, the…

A: Given that P(on time)=0.8 So, P(not on time)=1-P(on time)=1-0.8=0.2   P(burnt dinner)=P(on time and…

Q: A letter posted second-class on a Monday has the following probabilities of arriving on Tuesday to…

A: Let's approach this step by step:1) For the first-class letter, the probabilities are as follows:…

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A: Given The probability of selling a car is 1/20=0.05

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A: Given Data: P(V)=0.12 P(W)=0.63 P( V and W)=0.04

Q: Let A, B and C be three independent events such that P(A)= P(B)= 0.3 and P(C)=0.5. Find the…

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Q: = 0.23 and Assume that we have two events A and B, that are mutuUally exclusive. Assume further that…

A: we have two events A and B, that are mutually exclusive then A∩B=∅ and P(A∩B)=0 and given P(A)=0.23…

Q: Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is…

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Q: Suppose that X, Y, and 2 are jointly distributed random variables, that is, they are defined on the…

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A:

Q: The probability that an international flight leaving the United States is delayed in departing…

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A: Solution

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Q: We know that on a random day during the summer the probability that an adult in California goes to…

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A:

Q: Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is…

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Q: Let E be the event that a new car requires engine work under warranty and let T be the event that…

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Q: Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is…

A: PA∪B = PA + PB - PA∩BWhere,PA∪B = probability of event A or event BPA∩B = probability of event A and…

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A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

Q: 5.Prove the following properties of probability: P(A) = 1-P(A). b. For any events A and B, P(A U B)…

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A: Given Mentoring=0.43 Outreach=0.32

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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.