Question

Агрофирма закупает куриные яйца в двух домашних хозяйствах. 35% яиц из первого хозяйства — яйцавысшей категории, а из второго хозяйства — 55% яиц высшей категории. Всего высшую категорию получает 40% яиц. Найдите вероятность того, что яйцо, купленное у этой агрофирмы, окажется из первого хозяйства.

Answer 1

Х - вероятность того что яйцо купленное у этой агрофирмы окажется из первого хозяйства
1-х  -вероятность того что яйцо купленное у этой агрофирмы окажется из второго хозяйства
по формуле полной вероятности:
0.4х+0.2(1-х)=0.35
0.4х+0.2-0.2х=0.35
0.2х=0.35-0.2
0.2х=0.15
х=0.75

Answer 2

Problem Analysis

We are given that an agricultural firm purchases chicken eggs from two households. The eggs from the first household are of the highest quality, accounting for 35% of the total eggs, while the eggs from the second household are of a slightly lower quality, accounting for 55% of the total eggs. Additionally, we are told that 40% of the eggs purchased by the firm are of the highest quality. We need to find the probability that an egg purchased from this firm comes from the first household.

Solution

To find the probability that an egg purchased from this firm comes from the first household, we can use conditional probability. Let's denote the event that an egg comes from the first household as A, and the event that an egg is of the highest quality as B.

We are given the following probabilities: - P(A) = 35% = 0.35 (probability that an egg comes from the first household) - P(B|A) = 40% = 0.40 (probability that an egg is of the highest quality given that it comes from the first household) - P(B) = 40% = 0.40 (probability that an egg is of the highest quality)

We can use the formula for conditional probability to find P(A|B), the probability that an egg comes from the first household given that it is of the highest quality:

P(A|B) = P(A ∩ B) / P(B)

To find P(A ∩ B), the probability that an egg comes from the first household and is of the highest quality, we can use the multiplication rule:

P(A ∩ B) = P(B|A) * P(A)

Now we can substitute the given probabilities into the formulas to find the desired probability.

Calculation

Using the given probabilities: - P(A) = 0.35 - P(B|A) = 0.40 - P(B) = 0.40

We can calculate P(A ∩ B) and P(A|B) as follows:

P(A ∩ B) = P(B|A) * P(A) = 0.40 * 0.35 = 0.14

P(A|B) = P(A ∩ B) / P(B) = 0.14 / 0.40 = 0.35

Therefore, the probability that an egg purchased from this agricultural firm comes from the first household is 0.35 or 35%.

Answer

The probability that an egg purchased from this agricultural firm comes from the first household is 0.35 or 35%.