probability

5. A customer survey reported that 90% of new generation light bulbs still work after 5,000 hours and that 45% still work after 10,000 hours. If a light bulb still works after 5,000 hours, calculate the probability that it will last 5,000 hours more. 6. A lab invented a diagnostic test for COVID-19. Suppose the probability of a correct diagnostic is 0.9. Suppose that the prior in the population, the proportion of people who contracted the virus, is 0.5% (considering the rate in New York in April was about 500 cases per 100,000). (a) A person is chosen at random and tested. Calculate the probability that the test is positive. (b) What is the probability that a person has contracted the virus given that the test is positive