Question

Три стрелка независимо друг от друга стреляют по цели. Вероятность попадания в цель первым стрелком равна 0,7; вторым 0,7; третьим 0,4. Найдите вероятность того, что хотя бы один стрелок попадет в цель.

Answer 1

Ответ:

Один стрелок попадёт 18 раз

Answer 2

Problem Analysis

We are given three independent shooters who are each taking shots at a target. The probability of the first shooter hitting the target is 0.7, the probability of the second shooter hitting the target is 0.7, and the probability of the third shooter hitting the target is 0.4. We need to find the probability that at least one shooter hits the target.

Solution

To find the probability that at least one shooter hits the target, we can use the principle of complementary probability. The complementary probability of an event A is equal to 1 minus the probability of the event not happening (denoted as A'). In this case, the event A is that at least one shooter hits the target.

To find the probability that none of the shooters hit the target, we can multiply the probabilities of each shooter missing the target. Since the shooters are independent, we can multiply their probabilities together.

The probability that the first shooter misses the target is 1 - 0.7 = 0.3. The probability that the second shooter misses the target is 1 - 0.7 = 0.3. The probability that the third shooter misses the target is 1 - 0.4 = 0.6.

To find the probability that none of the shooters hit the target, we multiply these probabilities together: P(none of the shooters hit the target) = 0.3 * 0.3 * 0.6 = 0.054.

Finally, we can find the probability that at least one shooter hits the target by subtracting the probability that none of the shooters hit the target from 1: P(at least one shooter hits the target) = 1 - P(none of the shooters hit the target) = 1 - 0.054 = 0.946.

Therefore, the probability that at least one shooter hits the target is 0.946.

Conclusion

The probability that at least one shooter hits the target is 0.946.