Question

Вероятность попасть в мишень равна 0,6.произведено три выстрела.какова вероятность, что мишень была поражена один раз?

Answer 1

 попал выстрелом= 0.6
не попал=0.4
так-как мы вычитаем от 1 целого
ответ такой:
0,6*0,4*0,4=0,096

Answer 2

Problem Analysis

We are given that the probability of hitting the target is 0.6, and three shots are fired. We need to find the probability that the target is hit once.

Solution

To find the probability that the target is hit once, we can use the binomial probability formula. The formula is given by:

$$P(k) = C(n, k) \cdot p^k \cdot q^{n-k}$$

Where: - $P(k)$ is the probability of getting 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, - $q$ is the probability of failure on a single trial, and - $n$ is the total number of trials.

In this case, we have three trials, and the probability of success on a single trial is 0.6. Therefore, $n = 3$ and $p = 0.6$. The probability of failure on a single trial is $q = 1 - p = 1 - 0.6 = 0.4$.

Substituting these values into the formula, we can calculate the probability of hitting the target once:

$$P(1) = C(3, 1) \cdot 0.6^1 \cdot 0.4^{3-1}$$

Let's calculate this probability.

Calculation

Using the binomial probability formula, we can calculate the probability of hitting the target once:

$$P(1) = C(3, 1) \cdot 0.6^1 \cdot 0.4^{3-1}$$ $$P(1) = 3 \cdot 0.6 \cdot 0.4^2$$ $$P(1) = 3 \cdot 0.6 \cdot 0.16$$ $$P(1) = 0.288$$

Therefore, the probability of hitting the target once is 0.288 or 28.8%.

Answer

The probability that the target was hit once, given that the probability of hitting the target is 0.6 and three shots were fired, is 0.288 or 28.8%.