Question

Производится независимый пуск двух ракетпо цели. Найти вероятность поражения цели,если первая ракета поражает цель свероятностью 0,6, а вторая 0,8 Решите пожалуйста

Answer 1

Первая ракета не поразит цель с вероятностью p1=1-0,6=0,4
Вторая не поразит цель с вероятностью p2=1-0,8=0,2
Обе не поразят цель с вероятностью p3=0,4*0,2=0,08
Хотя бы одна поразит цель с вероятностью p=1-0,08=0,92

Answer 2

Problem Statement

We are given that two independent rockets are launched at a target. The first rocket has a probability of 0.6 of hitting the target, while the second rocket has a probability of 0.8 of hitting the target. We need to find the probability of hitting the target if the first rocket hits it.

Solution

To find the probability of hitting the target if the first rocket hits it, we can use conditional probability. Let's denote the event of the first rocket hitting the target as A, and the event of hitting the target overall as B. We want to find P(B|A), the probability of hitting the target given that the first rocket hits it.

The conditional probability formula states that:

P(B|A) = P(A and B) / P(A)

We know that P(A) is the probability of the first rocket hitting the target, which is given as 0.6. Now we need to find P(A and B), the probability of both rockets hitting the target.

Since the rockets are launched independently, the probability of both rockets hitting the target is the product of their individual probabilities:

P(A and B) = P(A) * P(B)

Substituting the given probabilities, we have:

P(A and B) = 0.6 * 0.8 = 0.48

Now we can substitute the values into the conditional probability formula:

P(B|A) = P(A and B) / P(A) = 0.48 / 0.6 = 0.8

Therefore, the probability of hitting the target if the first rocket hits it is 0.8.