Question

Срочно, помогите, прошу вас На соревнования приехали гимнастки из трёх стран. Из России 7 гимнасток, из Германии — 8, из Чехии — 5. Порядок выступлений гимнасток определяется жребием. Найдите вероятность того, что: а) первой будет выступать гимнастка из России; б) третьим по счёту будет выступление какой-нибудь гимнастки из Германии; в) второй по счёту будет выступать гимнастка из России или Чехии; г) последней будет выступать спортсменка, приехавшая не из Чехии.

Answer 1

а) 0,35

б) 0,4

в) 0,6

г) 0,75

Answer 2

Probability of Gymnasts' Performances

To find the probability of different scenarios for the gymnasts' performances, we can use the total number of gymnasts from each country and the total number of gymnasts overall.

Total number of gymnasts: - Russia: 7 - Germany: 8 - Czech Republic: 5

Total number of gymnasts overall: - 7 (Russia) + 8 (Germany) + 5 (Czech Republic) = 20

a) Probability of a Russian Gymnast Performing First

The probability that the first performer is from Russia can be calculated by dividing the number of Russian gymnasts by the total number of gymnasts.

Probability: - Number of Russian gymnasts: 7 - Total number of gymnasts: 20 - Probability = 7/20 = 0.35

b) Probability of a German Gymnast Performing Third

The probability that the third performer is from Germany can be calculated by dividing the number of German gymnasts by the total number of gymnasts.

Probability: - Number of German gymnasts: 8 - Total number of gymnasts: 20 - Probability = 8/20 = 0.4

c) Probability of a Russian or Czech Gymnast Performing Second

The probability that the second performer is from Russia or Czech Republic can be calculated by adding the number of Russian and Czech gymnasts, and then dividing by the total number of gymnasts.

Probability: - Number of Russian gymnasts: 7 - Number of Czech gymnasts: 5 - Total number of gymnasts: 20 - Probability = (7 + 5)/20 = 12/20 = 0.6

d) Probability of a Non-Czech Gymnast Performing Last

The probability that the last performer is not from the Czech Republic can be calculated by subtracting the number of Czech gymnasts from the total number of gymnasts, and then dividing by the total number of gymnasts.

Probability: - Number of Czech gymnasts: 5 - Total number of gymnasts: 20 - Probability = (20 - 5)/20 = 15/20 = 0.75

These probabilities represent the likelihood of the specified scenarios occurring during the gymnastics performances.