State whether the following probabilities can be reasonably approximated using Poisson probabilities (possibly by calculating the probability of some related event as well as expressing the actual requested probability in terms of it). If so, give a formula for approximation and measure the binomial probabilities and Poisson probabilities numerically. Let b(k, n, p) be the probability of exactly k successes in n independent trials with probability p of success on each trial.
(a) b(3,30,0.01)
(b) b(39,40,0.99)
(c) b(25,40,0.5).