Two Bernoulli processes with success probabilities p1 = 0.567 and p2 = 0.421 resulted from splitting a Bernoulli process. What was the success probability of the original Bernoulli process? Write the exact probability.
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- A new surgery is successfully 85% of the time . If the results of 7 such surgeries are randomly sampled, what is the probability that at least 5 of them are successful. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 51 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?A group of students is asked a question one at a time. Whether or not the students are able to answer the question correctly are independent Bernoulli trials with a 60% probability of the student questioned answering correctly. The expected number of students that needs to be questioned before getting three students who correctly answer the question is
- True or False: For a given experiment, it is possible to have two events A and B for which p(A) + p(B) > p(AUB). True FalseBoth flu and covid produce fevers. You know from past research that 10% of the population gets flu each year, but it is possible to get both covid and flu. Assume that the probability of getting flu and covid are independent. If this year the percentage of people reporting fever is 20%, what percentage of the population has covid? Studies show that due to similar transmission of flu and covid, someone who has covid has a 20% chance of also getting flu. What then is the probability of someone who has flu also having covid? Given the conditional information above, what is a better estimate of the percentage of people who have covid given the 20% fever reporting?Johnny carries out an experiment to study the lifespan of cockroach without water and food. At the end of day 0, he puts six cockroaches in different boxes respectively. On each day following, each cockroach has an equal chance to d ie with a probability of 0.5. What is the expected number of days until all six cockroaches die?
- A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 47 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect. The process improvement team agrees that the sample contains 27 bad items and 153 good items. The team gives the items to a “certified” operator for inspection. The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly. What is the probability that the inspector will reject an item? P(inspector will reject an item) = ________%. Enter value using one decimal place.the sales manager knows that 10% of his clients do not pay their debts in full. He supposes that he selects a sample of 100 clients. What is the probability that 14% or more will not be fulfilled in their obligations?