Question

Студентов выучил 13 вопросов из 20. На экзамене задают ему 3 вопроса. Какова вероятность того, что он ответит ровно на 2 вопроса. СРОЧНО ПОМОГИТЕ !

Answer 1

$P= \frac{C^2_{13}\cdot C_7^1}{C_{20}^3}= \frac{13\cdot 12\; \cdot 7\; \cdot 3!}{20\cdot 19\cdot 18\cdot \; 2!} \approx 0,4789$

Answer 2

Probability of Answering Exactly 2 Questions Correctly

To calculate the probability of the student answering exactly 2 questions correctly out of 3, we can use the binomial probability formula, which is:

P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where: - n = total number of trials (in this case, 3 questions) - k = number of successful trials (in this case, 2 questions answered correctly) - p = probability of success on an individual trial (in this case, the probability of answering a question correctly)

Calculation

Using the given information: - Total number of questions = 20 - Number of questions the student has learned = 13 - Probability of answering a question correctly = (13 + 2) / 20 = 15 / 20 = 0.75

Plugging these values into the formula: P(X=2) = (3 choose 2) * (0.75^2) * ((1-0.75)^(3-2))

P(X=2) = (3 choose 2) * (0.75^2) * (0.25^1)

P(X=2) = 3 * 0.5625 * 0.25

P(X=2) = 0.421875

Answer

The probability that the student will answer exactly 2 questions correctly is approximately 42.19%.