Question

В группе из 25 стрелков имеются 5 отличных , 15 хороших и 5 посредственных стрелков. Вероятность попадания в цель при одном выстреле для отличного стрелка равна 0,95; для хорошего - 0,15; для посредственного - 0,5. Найти вероятность того, что при одном выстреле двух стрелков из группы цель будет поражена.​

Answer 1

вот, это решение правильное)

Answer 2

Problem Analysis

We are given a group of 25 shooters, consisting of 5 excellent shooters, 15 good shooters, and 5 average shooters. The probability of hitting the target in one shot for an excellent shooter is 0.95, for a good shooter is 0.15, and for an average shooter is 0.5. We need to find the probability that both shooters hit the target in one shot.

Solution

To find the probability that both shooters hit the target in one shot, we need to consider the probabilities for each type of shooter and multiply them together.

Let's calculate the probability for each type of shooter:

- Probability for an excellent shooter: 0.95 - Probability for a good shooter: 0.15 - Probability for an average shooter: 0.5

Now, let's calculate the probability that both shooters hit the target in one shot:

- Probability for both shooters hitting the target = Probability for the first shooter hitting the target * Probability for the second shooter hitting the target

Since we have 5 excellent shooters, we can choose any two of them in 5C2 ways. Similarly, we can choose any two good shooters in 15C2 ways, and any two average shooters in 5C2 ways.

Therefore, the total probability can be calculated as follows:

Total probability = (Probability for excellent shooter)^2 * (Number of ways to choose 2 excellent shooters)
                  + (Probability for good shooter)^2 * (Number of ways to choose 2 good shooters)
                  + (Probability for average shooter)^2 * (Number of ways to choose 2 average shooters)

Let's calculate the total probability using the given values.

Calculation

Probability for excellent shooter = 0.95 Probability for good shooter = 0.15 Probability for average shooter = 0.5

Number of ways to choose 2 excellent shooters = 5C2 = 10 Number of ways to choose 2 good shooters = 15C2 = 105 Number of ways to choose 2 average shooters = 5C2 = 10

Total probability = (0.95)^2 * 10 + (0.15)^2 * 105 + (0.5)^2 * 10

Answer

The probability that both shooters hit the target in one shot is 0.3625.