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?

Answer 1

Ответ:

1/32

Пошаговое объяснение:

Если монету бросают 1 раз, то она может выпасть 2 способами: О и Р.

Если бросают 2 раза, то 2^2 = 4 способами: ОО, ОР, РО, РР.

И так далее.

Если монету бросают 5 раз, то получается 2^5 = 32 способа.

Из них нам подходит только один: ОООРР

Поэтому вероятность равна 1/32

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 that heads came up in the first three tosses.

Solution

To find the probability of getting heads in the first three tosses, we need to consider the possible outcomes where heads can occur in the first three tosses and tails occur twice in the remaining two tosses.

Let's break down the problem step by step:

1. The total number of possible outcomes when tossing a coin five times is 2^5 = 32, as each toss has two possible outcomes (heads or tails).

2. We know that tails came up exactly twice, so we need to find the number of outcomes where tails occur twice and heads occur in the first three tosses.

3. The number of ways to arrange two tails in three tosses is given by the binomial coefficient C(3, 2) = 3. This means there are three possible arrangements of two tails in the first three tosses.

4. For each of these three arrangements, the remaining two tosses can be either heads or tails. So, there are 2^2 = 4 possible outcomes for the remaining two tosses.

5. Therefore, the total number of outcomes where tails occur twice and heads occur in the first three tosses is 3 * 4 = 12.

6. Finally, the probability of getting heads in the first three tosses can be calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. So, the probability is 12/32 = 3/8.

Answer

The probability that heads came up in the first three tosses, given that tails came up exactly twice in five tosses, is 3/8.

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