Question

Вероятность выигрыша на один лотерейный билет равна 0,1. Найти вероятность того, что среди 8 приобретенных билетов будет 3 выигрышных.

Answer 1

Ответ:

см. ниже

Пошаговое объяснение:

Вероятность того, что из 9 билетов будет ровно 3 выигрышных, равна:

P=P9(3)=C39⋅0.13⋅0.96=0.0446.

Здесь число сочетаний

C39=9!3!⋅(9−3)!=9!3!⋅6!=7⋅8⋅91⋅2⋅3=84.

Ответ: 0.0446

Answer 2

Calculation of the Probability

To find the probability of having 3 winning tickets out of 8 purchased tickets, we need to use the binomial probability formula. The formula is as follows:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where: - P(X=k) is the probability of having exactly k successes - C(n, k) is the number of combinations of n items taken k at a time - p is the probability of success on a single trial - n is the total number of trials

In this case, the probability of winning on a single ticket is given as 0.1, and we want to find the probability of having exactly 3 winning tickets out of 8 purchased tickets.

Let's calculate the probability using the formula:

P(X=3) = C(8, 3) * 0.1^3 * (1-0.1)^(8-3)

Calculation Steps

1. Calculate the number of combinations: C(8, 3) = 8! / (3! * (8-3)!) = 56 2. Calculate the probability of success on a single trial: p = 0.1 3. Calculate the probability of failure on a single trial: 1-p = 1-0.1 = 0.9 4. Calculate the probability using the formula: P(X=3) = 56 * 0.1^3 * 0.9^5

Let's calculate the probability:

P(X=3) = 56 * 0.1^3 * 0.9^5

Using a calculator, we find that P(X=3) is approximately 0.2016.

Therefore, the probability of having exactly 3 winning tickets out of 8 purchased tickets is approximately 0.2016.