Question

В случайном эксперименте монету бросают трижды.найдите вероятность того,что орел выпадет ровно 3 раза

Answer 1

Есть несколько вариантов развития событий (всего их 8) :Орел Орел Орел
Орел Орел Решка                
1Орел Решка Решка
Решка Решка Решка
Решка Орел Орел                
2Решка Решка Орел
Орел Решка Орел                
3Решка Орел Решка



 Итак, вероятность того, что орёл выпадет ровно 2 раза = 3/8 = 0.375=37.5%

Answer 2

Calculating the Probability of Getting Three Heads in Three Coin Tosses

In a random experiment where a coin is tossed three times, the probability of getting heads (or "orel") exactly three times can be calculated using the binomial probability formula.

The formula for the binomial probability is: $$P = C(n, k) \cdot p^k \cdot (1-p)^{n-k}$$ Where: - $n$ is the number of trials (in this case, the number of coin tosses) - $k$ is the number of successful outcomes (in this case, the number of heads) - $p$ is the probability of success on each trial (in this case, the probability of getting heads)

Using this formula, we can calculate the probability step by step.

1. First, let's calculate the probability of getting heads in a single coin toss. From the search results, the probability of getting heads in a single coin toss is 0.5.

2. Now, we can use the binomial probability formula to calculate the probability of getting heads exactly three times in three coin tosses. - $n=3$ (number of coin tosses) - $k=3$ (number of heads) - $p=0.5$ (probability of getting heads in a single coin toss)

Plugging these values into the formula: $$P = C_3^3 \cdot (0.5)^3 \cdot (1-0.5)^{3-3}$$ $$P = 1 \cdot 0.5^3 \cdot 0.5^0$$ $$P = 0.125$$

Therefore, the probability of getting heads exactly three times in three coin tosses is 0.125.

So, the probability of getting heads (or "orel") exactly three times in three coin tosses is 0.125.

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