How to solve a probability problem, Bernoulli's scheme?

Question

Mathematics

There is a task: "There are 30 commercial banks in the city. Each has a 30% risk of bankruptcy within a year. Find the probability that the number of bankruptcies will be less than 15."
I know that using the Bernoulli scheme you can find the probability that there will be exactly 15 bankruptcies, for example. But since the condition is less than 15, then you need to find the sum of the probabilities P30(1) + P30(2) ... P30(14). But I'm not happy with the prospect of counting it all, so I want to know if it's possible to solve it in another way more concisely?

Answer 1

But I'm not happy with the prospect of counting it all, so I want to know if it's possible to solve it in another way more concisely?

Write a program, score in excel,
Task 6 (question b) Here's a look at how this type of task is solved

Answer 2

Yes, there is an approximate Moivre-Laplace formula.
https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%BA%D...
I have an example at the end of a recent note on Habré: https://habr.com/ru/ company/nerepetitor/blog/52681...