Question 4. Suppose that the probability of detecting a present mutation along a stretch of DNA is 0.9. Mutations are detected independently of one another. a) Given that there are three mutations present, what is the probability that exactly one is detected? b) Use the law of total probability to compute the probability that zero mutations are detected. c) Given that no mutations are detected, what is the probability that at least one mutation was present? d) Given that one mutation is detected, what is the probability that more than one mutation is present? Note that P(X55)=0.9994 when X\"Poisson(1). Therefore, you can assume that at most 5 mutations are present