Question

На международную конференцию по математике прибыло 3 человека из России, 5 из Индии и 2 из США. Порядок выступления определялся жребием. Найдите вероятность того, что последним будет выступать представитель США.

Answer 1

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Answer 2

Probability of the representative from the USA speaking last at the international mathematics conference

To find the probability that the representative from the USA will speak last at the international mathematics conference, we need to consider the total number of possible orders in which the representatives can speak.

Given that there are 3 representatives from Russia, 5 representatives from India, and 2 representatives from the USA, the total number of representatives is 3 + 5 + 2 = 10.

Since the order of the representatives is determined by drawing lots, each representative has an equal chance of being selected for any position in the order.

Therefore, the probability of the representative from the USA speaking last can be calculated as the ratio of the number of favorable outcomes (the USA representative speaking last) to the total number of possible outcomes.

The number of favorable outcomes is 1, as there is only one position for the last speaker.

The total number of possible outcomes is the total number of ways the representatives can be ordered, which is given by the factorial of the total number of representatives (10!):

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.

Therefore, the probability that the representative from the USA will speak last is:

P(USA speaking last) = 1 / 3,628,800.

Please note that the above calculation assumes that each representative can only speak once and that the order of the representatives is determined solely by drawing lots.