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

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.

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