# The probability of having a boy is 0.51. find the probability that among 100 newborns there will be 50 boys.

December 27, 2020 | education

| 1. The probability that a boy will be born: p = 0.51, and the probability that a girl is next in line: q = 0.49. Therefore, on average, among 100 newborns, there are 51 boys and 49 girls, which means that two girls lack boys.

2. This is only an average, but it is not always the same as the average, and it is possible that the number of boys and girls will coincide. We calculate the probability of this event using the Moivre-Laplace formula:

φ (x) – Gaussian function;

n = 100;

k = 50;

r = 1 / √ (npq) = 1 / √ (100 * 0.51 * 0.49) = 1 / √ (5.1 * 4.9) = 1 / √24.99 ≈ 0.2;

x = (k – np) r = (50 – 100 * 0.51) * 0.2 = (50 – 51) * 0.2 = -0.2;

P = r * φ (x) = 0.2 * φ (-0.2) = 0.2 * φ (0.2) ≈ 0.2 * 0.3910 = 0.0782.

Answer: 0.0782.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.