Question

В соревнованиях по толканию ядра участвуют 4 спортсмена из Дании, 3 спортсмена из Швеции, 4 спортсмена из Норвегии и 4 из Финляндии. Порядок в котором выступают спортсмены определяется жребием.Найдите вероятность того что спортсмен выступающий последним окажется из Швеции

Answer 1

4+3+4+4=15 спортсменов участвовало всего, кол-во всех исходов
3 спортсмена из Швеции - кол-во благоприятных исходов
Р(А)=3/15=1/5=0,2 вероятность, что спортсмен из Швеции последний

Ответ 0,2

Answer 2

Probability of a Swedish Athlete Performing Last

To find the probability that a Swedish athlete performs last in the shot put competition, we need to consider the total number of athletes and the number of Swedish athletes.

According to the information provided, there are 4 athletes from Denmark, 3 athletes from Sweden, 4 athletes from Norway, and 4 athletes from Finland participating in the competition.

The order in which the athletes perform is determined by drawing lots. Since there are a total of 15 athletes (4 from Denmark + 3 from Sweden + 4 from Norway + 4 from Finland), the probability of a Swedish athlete performing last can be calculated as the number of favorable outcomes (a Swedish athlete performing last) divided by the total number of possible outcomes.

To calculate the probability, we need to determine the total number of possible outcomes. Since the order is determined by drawing lots, there are n! (n factorial) possible outcomes, where n is the total number of athletes.

In this case, n = 15, so the total number of possible outcomes is 15!.

Now, we need to determine the number of favorable outcomes, which is the number of ways a Swedish athlete can perform last. Since there are 3 Swedish athletes, the number of favorable outcomes is 3!.

Therefore, the probability of a Swedish athlete performing last can be calculated as:

P(Swedish athlete performs last) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(Swedish athlete performs last) = 3! / 15!

Using the formula for factorial, we can simplify the expression:

P(Swedish athlete performs last) = 3 / 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Calculating this expression, we find that:

**P(Swedish athlete performs last) ≈ 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000#### Calculating the Probability To calculate the probability of a Swedish athlete performing last in the shot put competition, we can use the information provided about the total number of athletes from each country and the fact that the order is determined by drawing lots.

The total number of athletes is: - 4 from Denmark - 3 from Sweden - 4 from Norway - 4 from Finland

The total number of athletes is 4 + 3 + 4 + 4 = 15.

The probability of a Swedish athlete performing last can be calculated using the formula: \[ P(A) = \frac{n}{m} \] Where: - \( n \) is the number of favorable outcomes (in this case, a Swedish athlete performing last) - \( m \) is the total number of possible outcomes (in this case, the total number of athletes)

Applying the Formula

Using the formula, we can calculate the probability: \[ P(A) = \frac{n}{m} = \frac{3}{15} = \frac{1}{5} = 0.2 \]

Therefore, the probability of a Swedish athlete performing last in the shot put competition is 0.2 or 20%.