Probability Curves Showing Poisson's Exponential Summation

IN many importa nt practical operations the constant probability of an event happening in a single trial is extremely small. but the number of trials is so large that the event may actually occur a sufficient number of times to become a matter of importance. The curves of Figs. 1 and 2 show the probability P of such an event happening at least c times in a number of trials for which the average number of occurrences is a. The probability range shown is from 0.000001 to O.999999 and the average extends from 0 to 15 in Fig. 1 and to 200 in Fig. 2. An open scale is obtained at both ends, even when the probability approaches to within one part in a million of the limits 0 and 1, by employing an ordinate scale corresponding to the normal probability integral.