Prove that the sum of the probabilities of all possibilities in two independent events amounts to certainty.
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A: here define event R = red card G= Green card B= Blue card
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A: Consider that, equally likely for a couple to have a boy or a girl. (a) Consider that couple has…
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Q: Events A and B are consistent and their probabilities are not equal to zero. Which statement is…
A: Two events are said to be consistent if, P(A∩B) < P(A) and P(A∩B) < P(B) P(A∪B) > P(A) and…
Q: A man must put 8 balls in a box - some white and some black. He will then pull out three. How many…
A: Given a man puts 8 balls in a box. We have to find the probability.
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A: Given that: Total number of passengers on the bus = 6 And there are 6 remaining stops before the end…
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Q: The break in an electric circuit occurs when at least one out of three elements connected in series…
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Q: Suppose A and B are two independent events. Prove A' and B are independent events. (Note: this is…
A: Given A and B are independent
Q: Two independent events occur , A and B which have probabilities of 0.2 and 0.4 what is the…
A: The probability of event A is 0.2, the probability of not happening of event A is 0.8=1-0.2. The…
Q: The probability that the mean height for the sample is greater than 65 inches is (Round to four…
A: It is given that Mean, μ = 64.2 Sample size, n = 65 Standard deviation, σ = 2.55
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A: Given Probabilities of each element in a series circuit that it will go out of order.we need to…
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Q: Suppose, Tonmoy, Sneha and Rashed are three friends who applied for a job in a company where the…
A: Given probability distribution is P(T) =2/3 P(S) =1/3 P(R) =4/7
Q: Will be (a) What is the probability that none of the balloons in a packet will be defective? (b)…
A: Here AS PER guidelines I HAVE CALULATED 3 subparts here p = probability of defective balloon =…
Q: 3. What are events in which the probability of one event occurring is not affected by the occurrence…
A: Mutually Exclusive events: The probability of one event occurring is not affected by the occurrence…
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A: Let the events of enjoying weather at Murree and Abbottabad be M and A. PM=0.5,PA=0.12 Since the…
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Q: XYZ auto insurer company offers an auto insurance plan to the employees of a company. The employees…
A: The company offers an auto insurance plan of a company. The employees cannot choose exactly two of…
Q: suppose that in a certain part of the world the probability a random person like hershey kisses milk…
A: Step 1: Let us take that the person likes hershey kisses milk chocolate as A, and The person likes…
Q: A group of 7 men are meeting for lunch. (a) Each of the 7 men is wearing a coat when they enter the…
A: As per guidelines we will solve first question only, please repost other questions for more answers.…
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Q: In a country, 75% of the graduates are citizens,60% of the citizens graduates are employed while…
A: Given , 75 percent of the graduates are citizens ... Among them 60 percent of citizens are employed…
Q: It has been claimed that at least 40% of all the personal bankruptcies in the United States are due…
A: given data P(bankcrupt) = p = 0.40 sample size (n) = 10 x = no. of bankcrupties P(x≥4) = ?
Q: Determine the probabilities of having (i) at least 1 girl and (ii) at least 1 girl and 1 boy in a…
A: i) Suppose event B defines that the child is a boy and event G defines that the child is a girl.
Q: Two local factories produce microwaves. Each microwave produced at factory A is defective with…
A: The following solution is provided below
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A: Let T be the time it takes to reach the city and Ai be the event that the tourist chooses road I for…
Q: The break in an electric circuit occurs when at least one out of three elements connected in series…
A: Answer:
Q: Assuming that every time you roll dice the events are independent of each other (meaning that one…
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Q: Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown…
A: Given the different possible poker hands and their winning chances. Also given that all of these…
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- A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, then find the probability that the other is also good.One of the n encrypted files in a folder is a special file. K of these files are removed one at a time by an attacker who has access to the folder. Each choice has an equal chance of being any of the currently available files. What is the probability that the person will withdraw the special file?You must justify or explain how you arrived at your conclusion.Two machines turn out all the products in a factory, with the first machine producing 35% of the product and the second 65%. The first machine produces defective products 7% of the time and the second machine 2% of the time (a) What is the probability that a defective part is produced at this factory given that it was made on the first machine?
- A student is selected at random from a list of all enrolled students at HarvardUniversity. Suppose the probability that the student is female is 0.48 and the probability that the student has a part-time job is 0.75. (a) In this context, define two events A and B. Also write down P(A) and P(B).(b) What does it mean, in this context, for A and B to be disjoint events?(c) Calculate P(A)+ P(B). Hence, or otherwise, explain why A and B cannot be disjoint events.What is the likelihood of a randomly selected student in a school of 500 having both a parent who is a doctor and a parent who is a lawyer, given that 10% of the parents in the school are doctors, 15% are lawyers, and 3% are both doctors and lawyers? How can the probability be calculated using the formula for conditional probability?In a district, 65% of the total population is in favor of rising the traffic challan. During a survey of that region,you sample 100 people. Then find the probability that those people who participated in survey will contain(a) between 60 and 70 inclusive who are in favor;(b) at least 50 who are in favor of the proposition;(c) Less than 75 in favor.
- Suppose we define A as the event of obtaining {1, 3, 5}, and event B as the set {1,5,6}.(a) Are events A and B mutually exclusive events? Why or why not?(b) Are events A and B independent events? Why or why not?(c) What are the complements of events A and B, respectively, and their probabilities?Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that she or he has 6 children. What is the probability that at least one is a boy given that at least 5 of the children are girls?What is the known probability when two events will both occur, such that the probabilities of the individual events are from its product? A. Independent Event B. Dependent Event C. Individual Event D. Intersection of Event Mr. Chua has two children. What is the probability that they are both boys? А. 1/2 В. 1/3 C. 1/4 D. 1
