Let 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 either fails or shows strain during the test?

In the sport of basketball, a player will sometimes get the opportunity to shoot two free throws without being affected by any other players in the game.  Assume that, for one player, these two free throws are independent of each other.  If this player makes free throws 80% of the time, what is the probability that this player will make neither free throw in the opportunity?

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?

A disease afflicts 1 person in 10 in a population. A test for this disease results in 5% false positives. Assume that a random person is tested for the disease (this person is not selected for the test because there are other symptoms indicating the presence of the disease nor are there any special signs of being disease free). Assume that there are no false negatives from this test. A person tests positive. What is the probability that the person truly has the disease?   Now assume that false negatives are 15%. What is the probability that the person truly has the disease?   The following paragraph is taken from the National Cancer Institute’s web site on the PSA test for prostate cancer. The paragraph is the complete discussion of false positive PSA results offered on the web site.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the virus, blood samples from 15 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.

The probability that an international flight leaving the United States is delayed in departing (event D) is .36. The probability that an international flight leaving the United States is a transpacific flight (event P) is .25. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .09.   (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.)