Question

В ящик, содержащий 2 одинаковые детали, брошена стандартная деталь того же вида, а затем наудачу взята одна деталь. Найти вероятность того, что эта деталь будет стандартной, если все предположения о начальном количестве стандартных деталей в ящике равновозможны.

Answer 1

Сначало было 2 детали, потом добавили ещё одну, стало 3. Вероятность того что наугад взятая деталь будет стандартной равна 1/3=0,333...

Answer 2

Calculating the Probability of Drawing a Standard Part

To calculate the probability of drawing a standard part from a box containing 2 identical parts, where a standard part is initially thrown into the box and then one part is randomly drawn, we can use the following approach:

1. Initial Conditions: - The box contains 2 identical parts. - A standard part is thrown into the box. - One part is then randomly drawn from the box.

2. Calculating the Probability: - The probability of drawing a standard part can be calculated using the concept of conditional probability. - Let's denote the events as follows: - A: The first part thrown into the box is standard. - B: The part drawn from the box is standard. - We want to find P(B|A), the probability of drawing a standard part given that the first part thrown into the box is standard.

3. Applying Conditional Probability Formula: - The conditional probability formula states: - P(B|A) = P(A ∩ B) / P(A) - Here, P(A ∩ B) represents the probability that both events A and B occur, and P(A) is the probability of event A.

4. Using the Given Information: - From the given information, we know that the initial quantity of standard parts in the box is equally likely.

5. Calculating the Probability: - We can calculate the probability of drawing a standard part using the given information and the conditional probability formula.

Probability Calculation

The probability of drawing a standard part, given the initial conditions, can be calculated as follows:

- P(A) = Probability of the first part thrown into the box being standard. - P(B|A) = Probability of drawing a standard part given that the first part thrown into the box is standard.

Using the given information and the conditional probability formula, we can calculate the probability of drawing a standard part from the box.