Question

Вероятность получить за некоторый курс по математике отличную отметку составляет 0,3. Какова вероятность того, что среди семи случайно выбранных студентов более четырех не будут иметь за этот курс отличную оценку?

Answer 1

Ответ:

я не знаю

Пошаговое объяснение:

советую учиться!

Answer 2

Probability of Getting an Excellent Grade

The probability of getting an excellent grade in a certain math course is 0.3. We want to find the probability that among seven randomly selected students, more than four will not have an excellent grade in this course.

To solve this problem, we can use the binomial distribution formula. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials.

In this case, the number of trials is seven (as we are selecting seven students), and the probability of success (getting an excellent grade) is 0.3.

Let's calculate the probability using the binomial distribution formula:

P(X > 4) = 1 - P(X ≤ 4)

Where: - P(X > 4) is the probability of having more than four students without an excellent grade. - P(X ≤ 4) is the probability of having four or fewer students without an excellent grade.

To calculate P(X ≤ 4), we need to sum the probabilities of having 0, 1, 2, 3, and 4 students without an excellent grade.

Now, let's calculate the probabilities step by step:

1. Probability of having 0 students without an excellent grade: - P(X = 0) = (7 choose 0) * (0.3^0) * (0.7^7) = 0.7^7 = 0.0823543

2. Probability of having 1 student without an excellent grade: - P(X = 1) = (7 choose 1) * (0.3^1) * (0.7^6) = 7 * 0.3 * 0.7^6 = 0.2334744

3. Probability of having 2 students without an excellent grade: - P(X = 2) = (7 choose 2) * (0.3^2) * (0.7^5) = 21 * 0.3^2 * 0.7^5 = 0.3086997

4. Probability of having 3 students without an excellent grade: - P(X = 3) = (7 choose 3) * (0.3^3) * (0.7^4) = 35 * 0.3^3 * 0.7^4 = 0.2319174

5. Probability of having 4 students without an excellent grade: - P(X = 4) = (7 choose 4) * (0.3^4) * (0.7^3) = 35 * 0.3^4 * 0.7^3 = 0.1210608

Now, let's calculate P(X ≤ 4):

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0823543 + 0.2334744 + 0.3086997 + 0.2319174 + 0.1210608 = 0.9775066

Finally, we can calculate P(X > 4):

P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.9775066 = 0.0224934

Therefore, the probability that among seven randomly selected students, more than four will not have an excellent grade in this math course is approximately 0.0224934.