The probability of winning for one lottery ticket is 0.01. What is the likelihood that among 15 purchased

The probability of winning for one lottery ticket is 0.01. What is the likelihood that among 15 purchased tickets there will be at least two winning tickets?

The probability that the lottery ticket is winning p = 0.01;
Probability of a ticket without a win:
q = 1 – p = 1 – 0.01 = 0.99.
First, we find the probability of the opposite event, that among n = 15 purchased tickets there are fewer than two winning ones, that is, that there is one winning ticket or not.
P (<2) = P (0) + P (1);
According to Bernoulli’s formula:
P (0) = C (15.0) * p ^ 0 * q ^ 15 = 1 * 1 * 0.99 ^ 15 = 0.86;
P (1) = C (15.1) * p ^ 1 * q ^ 14 = 15 * 0.01 * 0.99 ^ 15 = 0.13;
P (<2) = 0.86 + 0.13 = 0.99.
The probability of an opposite event such that among n = 15 purchased tickets at least 2 are winning:
P (≥2) = 1 – P (<2) = 1 – 0.99 = 0.01.
Answer: 0.01.