Question

В показательных выступлениях по фигурному катанию участвуют 4 девушки и 5 юношей. Порядок выступления определяется жеребьевкой. Найдите вероятность того, что первые две выступают девушки.

Answer 1

Решение
1. Число возможных исходов N = 9
Число исходов опыта, в которых наступает событие А
 ( первой выступает девушка ) N(A)=4.
Вероятность Р ( А ) = 4/9
2. Число возможных исходов
( после выборки первого выступающего ) N =8
Число исходов опыта, в которых наступает событие В
( второй выступает девушка ) N( В )=3.
 Вероятность Р ( В )=3/8
3. Р ( А + В )= 4/9+3/8=1/6 

Answer 2

Probability of the first two performances being by girls in figure skating

To find the probability that the first two performances are by girls in figure skating, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Given that there are 4 girls and 5 boys participating in the figure skating performances, the total number of participants is 9.

To determine the number of favorable outcomes, we need to calculate the number of ways to choose 2 girls from the 4 available. This can be done using combinations. The formula for combinations is:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of items and k is the number of items to be chosen.

In this case, we want to choose 2 girls from the 4 available, so the calculation becomes:

C(4, 2) = 4! / (2!(4-2)!) = 6

Therefore, there are 6 favorable outcomes where the first two performances are by girls.

The total number of possible outcomes is the number of ways to arrange all 9 participants. This can be calculated using permutations. The formula for permutations is:

P(n) = n!

Where n is the total number of items.

In this case, we want to arrange all 9 participants, so the calculation becomes:

P(9) = 9! = 362,880

Therefore, there are 362,880 possible outcomes.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes = 6 / 362,880

The probability that the first two performances are by girls in figure skating is approximately 0.0000165.

Please note that the above calculation assumes that the order of the performances matters and that each participant can only perform once. If there are additional constraints or information, please let me know for a more accurate calculation.