Question

Двое соперников участвует в олимпиаде. Вероятность того, что первый решит все задачи верно равна 0,89. Для второго эта вероятность равна 0,92. Найти вероятность того, что только один займет первое место. Помогите пожалуйста, очень надо!!!

Answer 1

Ответ:

0,1724

Объяснение:

Answer 2

Problem Analysis

We are given that two competitors are participating in an Olympiad. The probability that the first competitor solves all the problems correctly is 0.89, and the probability that the second competitor solves all the problems correctly is 0.92. We need to find the probability that only one of them will take the first place.

Solution

To find the probability that only one of the competitors will take the first place, we need to consider two cases: 1. The first competitor solves all the problems correctly, and the second competitor does not. 2. The first competitor does not solve all the problems correctly, and the second competitor does.

Let's calculate the probabilities for each case and then add them together to get the final probability.

Case 1: The first competitor solves all the problems correctly, and the second competitor does not.

The probability of the first competitor solving all the problems correctly is given as 0.89. The probability of the second competitor not solving all the problems correctly can be calculated as 1 - 0.92 = 0.08.

The probability of both events happening together (the first competitor solving all the problems correctly and the second competitor not solving all the problems correctly) can be calculated by multiplying their individual probabilities: 0.89 * 0.08 = 0.0712.

Case 2: The first competitor does not solve all the problems correctly, and the second competitor does.

The probability of the first competitor not solving all the problems correctly can be calculated as 1 - 0.89 = 0.11. The probability of the second competitor solving all the problems correctly is given as 0.92.

The probability of both events happening together (the first competitor not solving all the problems correctly and the second competitor solving all the problems correctly) can be calculated by multiplying their individual probabilities: 0.11 * 0.92 = 0.1012.

Final Probability

To find the probability that only one of the competitors will take the first place, we need to add the probabilities from both cases: 0.0712 + 0.1012 = 0.1724.

Therefore, the probability that only one of the competitors will take the first place is 0.1724.

Please note that the above calculations are based on the given probabilities and assumptions made in the problem statement.