Question

В милицейском колледже города Брюкова экзамены сдают так. Студент выбирает пять вопросов и получает столько баллов, на сколько вопросов он правильно ответил. Студент Громов знает 15 вопросов из 24. Какова вероятность того, что он получит пятерку?решение

Answer 1

15/24=0.625
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Answer 2

Probability of Getting a Perfect Score in the Police College Exam

In the given scenario, the student Gromov knows 15 questions out of 24 and chooses 5 questions to answer. We can calculate the probability of him getting a perfect score (i.e., answering all 5 questions correctly) using the concept of combinations and probability.

To calculate the probability, we can use the formula for the probability of getting exactly k successes in n trials, where the probability of success on each trial is p.

Calculation

The probability of getting a perfect score can be calculated using the formula:

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

Where: - n = total number of questions chosen - k = number of questions answered correctly - p = probability of answering a question correctly

In this case, n = 5 (as the student chooses 5 questions to answer), k = 5 (as he wants to answer all 5 questions correctly), and p = 15/24 (as he knows 15 out of 24 questions).

Applying the Formula

Substituting the values into the formula:

P(X = 5) = (5 choose 5) * ((15/24)^5) * ((9/24)^0)

Using the combination formula (n choose k) = n! / (k! * (n-k)!) and simplifying:

P(X = 5) = (5! / (5! * 0!)) * ((15/24)^5) * (1)

P(X = 5) = (1) * ((15/24)^5)

Calculating the Probability

Let's calculate the probability using the given values.

P(X = 5) = (15/24)^5

P(X = 5) ≈ 0.0796

Conclusion

The probability of the student Gromov getting a perfect score (answering all 5 questions correctly) is approximately 0.0796, or about 7.96%.

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