Consider randomly selecting a student at a large university, and let A be theevent that the selected student has a Visa card and B be the analogous event forMasterCard. Suppose that P(A) = 0.6 and P(B) = 0.4. It could be the case that P(AN B) = 0.5.Select one:O TrueFalse

Given P(A) = 0.6 P(B) = 0.4 P(A ∩ B) = 0.5

Answered: Consider randomly selecting a student…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that E and F are two events and that P(E and F) = 0.2 and P(E) = 0.5. What is P(F|E)? ... P(F|E) = (Type an integer or a decimal. Do not round.)
Recently, Hector ran for president of the local school board. Of those who voted in the election, 80% had a high school diploma, and the other 20% did not. Hector got 65% of the vote of those with high school diplomas, while he got only 25% of the vote of those without high school diplomas. Let D denote the event that a randomly chosen voter (in the school board election) had a high school diploma and D denote the event that a randomly chosen voter did not have a high school diploma. Let H denote the event that a randomly chosen voter voted for Hector and H denote the event that a randomly chosen voter did not vote for Hector. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses. (If necessary, consult a list of formulas.)
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Suppose that 12% of a certain batch of calculators have a defective case, and that 16% have defective batteries. Also, 4% have both a defective case and defective batteries. A calculator is selected from the batch at random. Find the probability that the calculator has a good case and good batteries. The probability that the calculator has a good case and good batteries is (Type an integer or a decimal.) C
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4) Determine whether the given set of functions is linearly independent on the interval (-x,). a) (z) = cos 2z, (2) = 1, 1,()= cos z b) (z)=z, 1,(2)=z-1, (z)=z+3 c) ()=e**, 1,(=)=e
Given P(A) = 0.2 and P(B) = 0.4, do the following. a) If A and B are mutually exclusive events, compute P(A or B). b) If P(A and B) = 0.1, compute P(A or B).
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a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery service?
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?

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Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.6 and P(B) = 0.4. It could be the case that P(A N B) = 0.5. Select one: O True O False