Question

Три стрелка делают по одному выстрелу, вероятность попадания при этом 0,5; 0,6; 0,8. Найти вероятность того, что хотя бы один из них промахнется. (с объяснением)

Answer 1

1. находим вероятность,что промахнутся все три: 0,5*0,6*0,8=0,24
далее вероятность(хотя бы один)=1-0,24=0,76
ответ:0,76

Answer 2

Problem Analysis

We are given that three shooters take turns firing one shot each, with probabilities of hitting the target being 0.5, 0.6, and 0.8 respectively. We need to find the probability that at least one of them misses the target.

Solution

To find the probability that at least one shooter misses the target, we can use the principle of complementary probability. We will find the probability that all three shooters hit the target and subtract it from 1.

Let's denote the probabilities of hitting the target for the three shooters as p1, p2, and p3, and the probabilities of missing the target as q1, q2, and q3 respectively.

Using the principle of complementary probability, the probability that all three shooters hit the target is given by:

P1 = p1 * p2 * p3

Therefore, the probability that at least one shooter misses the target is:

P = 1 - P1

Now, let's substitute the given probabilities and calculate the result.

Calculation

Given probabilities: - p1 = 0.5 - p2 = 0.6 - p3 = 0.8

We can calculate the probabilities of missing the target as: - q1 = 1 - p1 = 1 - 0.5 = 0.5 - q2 = 1 - p2 = 1 - 0.6 = 0.4 - q3 = 1 - p3 = 1 - 0.8 = 0.2

Using the formula for P1, we have: P1 = p1 * q2 * q3 + q1 * p2 * q3 + q1 * q2 * p3

Substituting the values, we get: P1 = 0.5 * 0.4 * 0.2 + 0.5 * 0.6 * 0.2 + 0.5 * 0.4 * 0.8 = 0.04 + 0.06 + 0.16 = 0.26

Finally, substituting the value of P1 into the formula for P, we get: P = 1 - P1 = 1 - 0.26 = 0.74

Therefore, the probability that at least one shooter misses the target is 0.74.

Answer

The probability that at least one of the three shooters misses the target is 0.74.