udget Airlines is a seasonal airline that operates flights from Myrtle Beach, South Carolina, to various cities in the northeast. Recently Budget has been concerned about the number of lost bags. Ann Poston from the Analytics Department was asked to study the issue. She randomly selected a sample of 500 flights and found that a total of twenty bags were lost on the sampled flights. What is the probability that none of the bags were lost? Round your answer to four decimal places.

We believe that 77% of the population of all Business Statistics students consider statistics to be an interesting topic. Suppose we randomly and independently select 24 students from the population. If the actual percentage is really 77%, find the probability of observing 23 or more students who find statistics to be an interesting topic. Round to six decimal places.

please answer the question down below!

A sample of 2500 patients were taken to assess a medical test.  40% of the sample had a positive test, 563 patients have the disease and tested negative, and 235 patients do not have the disease and tested positive. What is the probability someone has a positive test if it is known they do have the disease?  (round your answer to 4 decimal places) What is the probability someone does not have the disease if their test is known to be negative?  (round your answer to 4 decimal places)