Question

Дана симметричная монет - при каждом ее подбрасывании выпадение орла или решки равновероятно. Эту монету подбросили пять раз. Известно, что решка выпала ровно 2 раза. Какова вероятность, что при первых трех подбрасываниях монеты выпал орел? Даю сотку

Answer 1

Ответ:

Это вне зависимости от выпадения решки равна произведению вероятности выпадения орла

$P = ( \frac{1}{2} ) \times ( \frac{1}{2} ) \times ( \frac{1}{2} ) = \frac{1}{8} = 0.125$

Шанс выпадения 0.125

Answer 2

Problem Analysis

We are given a symmetric coin, where the probability of getting heads (орел) or tails (решка) is equal. The coin is tossed five times, and we know that tails came up exactly twice. We need to find the probability of getting heads on the first three tosses.

Solution

To find the probability of getting heads on the first three tosses, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Let's break down the problem step by step:

1. Total number of possible outcomes: - Since the coin is tossed five times, each toss has two possible outcomes (heads or tails). - Therefore, the total number of possible outcomes is 2^5 = 32.

2. Number of favorable outcomes: - We know that tails came up exactly twice in the five tosses. - To find the number of favorable outcomes, we need to determine the number of ways we can arrange two tails and three heads in the first three tosses. - This can be calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n-k)!), where n is the total number of tosses and k is the number of tails. - In this case, n = 3 (the first three tosses) and k = 2 (the number of tails). - Therefore, the number of favorable outcomes is C(3, 2) = 3.

3. Probability calculation: - The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. - Therefore, the probability of getting heads on the first three tosses is 3/32.

Answer

The probability of getting heads on the first three tosses, given that tails came up exactly twice in the five tosses, is 3/32.

Please note that this answer is based on the information provided and assumes that the coin is fair and unbiased.

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