Question

В классе учатся 15 девочек и 10 мальчиков. Двух учеников вызвали к доске. Какова вероятность того что у доски окажутся 2 девочки

Answer 1

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Answer 2

Probability of Two Girls Being Called to the Board

To calculate the probability of two girls being called to the board, we need to consider the total number of students in the class and the number of girls in the class.

Given that there are 15 girls and 10 boys in the class, the total number of students is 25.

To calculate the probability, we need to determine the number of ways we can choose 2 girls from the total number of girls in the class, which is 15.

The formula to calculate the probability is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the number of favorable outcomes is the number of ways we can choose 2 girls from the total number of girls, which can be calculated using the combination formula:

Number of favorable outcomes = C(15, 2)

Where C(n, r) represents the number of combinations of n items taken r at a time.

The total number of possible outcomes is the total number of ways we can choose any 2 students from the class of 25, which can be calculated using the combination formula:

Total number of possible outcomes = C(25, 2)

Now, let's calculate the probability:

Probability = C(15, 2) / C(25, 2)

Using the combination formula, we can calculate the number of combinations:

C(15, 2) = 15! / (2! * (15-2)!) = 15! / (2! * 13!) = (15 * 14) / (2 * 1) = 105

C(25, 2) = 25! / (2! * (25-2)!) = 25! / (2! * 23!) = (25 * 24) / (2 * 1) = 300

Therefore, the probability of two girls being called to the board is:

Probability = 105 / 300 = 0.35

So, the probability is 0.35 or 35%.

Please note that the above calculation assumes that the selection of students to go to the board is random and unbiased.