Question

Два стрелка независимо друг от друга стреляют в цель. Вероятность попадания в цель первого стрелка равна 0,8, а второго - 0,7. Какая вероятность того, что один стрелок промахнется, а другой - попадет? С объяснением пожалуйста, заранее спасибо.

Answer 1

Вероятность промаха 1_го 20%,попадания 2_го 70%

Answer 2

Problem Analysis

We are given that two shooters independently shoot at a target. The probability of the first shooter hitting the target is 0.8, and the probability of the second shooter hitting the target is 0.7. We need to find the probability that one shooter misses while the other hits.

Solution

To find the probability that one shooter misses while the other hits, we can use the formula for the probability of the intersection of two independent events. Let's denote the event of the first shooter hitting the target as A1 and the event of the second shooter hitting the target as A2.

According to the formula, the probability of both events A1 and A2 occurring is given by: P(A1 ∩ A2) = P(A1) * P(A2) -- (1)

We are interested in the probability that one shooter misses while the other hits. Let's denote the event of the first shooter missing as A1' and the event of the second shooter hitting as A2.

The probability of one shooter missing while the other hits is given by: P(A1' ∩ A2) = P(A1') * P(A2) -- (2)

To find P(A1' ∩ A2), we need to calculate P(A1') and P(A2) separately.

From the given information, we know that the probability of the first shooter hitting the target is 0.8, so the probability of the first shooter missing is 1 - 0.8 = 0.2. Similarly, the probability of the second shooter hitting the target is 0.7, so the probability of the second shooter missing is 1 - 0.7 = 0.3.

Now, we can substitute these values into equation (2) to calculate the probability of one shooter missing while the other hits.

P(A1' ∩ A2) = P(A1') * P(A2) = 0.2 * 0.7 = 0.14

Therefore, the probability that one shooter misses while the other hits is 0.14.

Answer

The probability that one shooter misses while the other hits is 0.14.

Explanation

When two shooters independently shoot at a target, the probability of one shooter missing while the other hits can be calculated using the formula for the intersection of two independent events. In this case, we have the event of the first shooter missing (A1') and the event of the second shooter hitting (A2).

By substituting the probabilities of the first shooter missing (0.2) and the second shooter hitting (0.7) into the formula, we find that the probability of one shooter missing while the other hits is 0.14.

Please let me know if anything is unclear or if you need further assistance!