et Event A be that the component fails a particular test and Event B be that the component strains but does not fail. Event A occurs with a probability of 0.30, and Event B occurs with a probabaility of 0.24. What is the probability that the component works perfectly well during the test (i.e. neither fails or shows signs of strain)?

A diagnostic test for disease X correctly identifies the disease 88% of the time. False positives occur 11%. It is estimated that 2.78% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities.                                                                                                                                                                                                                                                                                                   The percentage chance that, given a negative result, the person does not have disease X=                                        The percentage chance that, the person will be misclassified =

The probability that an international flight leaving the United States is delayed in departing (event D) is .32. The probability that an international flight leaving the United States is a transpacific flight (event P) is .50. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .16. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.) may I get a breakdown on how to find the answer to this question please?

Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?

Suppose you are told that among Atlantic salmons, the proportion of salmons suffering from a viral infection is 0.085.    If you collect a sample 250 Atlantic salmons, what is the chance that the proportion of salmons in your sample suffering from a viral infection will be less than 0.9?  Would you expect the probability of the event in (1) to be higher or lower if you had a sample of 500 salmons instead? Justify.

A medical treatment has success rate of 0.8 two patient will be treated with this treatment, assuming the results are independent. For the two patients what is the probability that neither one of them will be successfully cured O 0.36 O 0.04 O None O 0.64

A state government hired a contractor for a road-construction project. The contractor's type, its cost efficienciency, is unknown to the government. There is 2/3 probability of the its construction cost being 3 (billion dollars per lane) and 1/3 probability of the cost being 5. More lanes yield more social benefit in the form of faster travel and fewer accidents. The social value V (measured in billions of dollars) from having N lanes on the highway is: V-15N-N?/2. The government is interested in choose N and writing a contract to maximize the benefit to the state (V) net of the fee paid to the contractor (call it F); G-V-F. Your goal as a government official is to design a pair of contracts to separate the types of contractor. You want the contractor to choose "Contract L: Build N lanes and get paid RL dollars" if its cost type is low cost of $3 (billion dollars per lane) and to choose "Contract H: Build NH lanes and get paid RH dollars" if its cost type is high cost $5 (billion…

A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.75; that is, the probability that it will activate the sprinkler when it should is 0.75. The other type, which operates independently of the first type, has a reliability of 0.85. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head. (provide your answer in four decimal numbers) (i) What is the probability that the sprinkler head will be activated? (1.5) (ii) What is the probability that the sprinkler head will not be activated? (1.5) (iii) What is the probability that both activation devices will work properly? (1.5) (iv) What is the probability that only the device with reliability 0.75 will work properly? (1.5)