Question

Одна вакцина формирует иммунитет по отношению к краснухе в 95% случаев. Предположим, что вакцинировалось 30% популяции и что вероятность заболеть краснухой у вакцинированного человека без иммунитета такая же, как и у невакцинированного. Какова вероятность того, что человек, заболевший краснухой, был вакцинирован?

Answer 1

Ответ:

Пошаговое объяснение:

возмем пример 10000 человек

30% вакцинир. это 3000

70% невакцинир. 7000

из числа вакцинир. 5% не иммунит.

это 3000×0,05=150 чел

Всего заболеют 7000+150=7150

требуемая вероятность =

= 150÷ 7150=0,021

Answer 2

Calculation of the Probability

To calculate the probability that a person who has contracted rubella (also known as German measles) has been vaccinated, we need to consider the information provided.

According to the statement, a single vaccine provides immunity against rubella in 95% of cases. Additionally, 30% of the population has been vaccinated. It is assumed that the probability of contracting rubella for a vaccinated person without immunity is the same as that for an unvaccinated person.

To calculate the probability, we can use Bayes' theorem, which states:

P(A|B) = (P(B|A) * P(A)) / P(B)

Where: - P(A|B) is the probability of event A occurring given that event B has occurred. - P(B|A) is the probability of event B occurring given that event A has occurred. - P(A) is the probability of event A occurring. - P(B) is the probability of event B occurring.

In this case, event A is being vaccinated, and event B is contracting rubella.

Let's calculate the probability step by step.

Step 1: Define the Events

Let's define the events: - A: Being vaccinated - B: Contracting rubella

Step 2: Calculate the Probability of Being Vaccinated (P(A))

According to the information provided, 30% of the population has been vaccinated. Therefore, the probability of being vaccinated is 0.3.

P(A) = 0.3

Step 3: Calculate the Probability of Contracting Rubella Given Vaccination (P(B|A))

According to the statement, the probability of contracting rubella for a vaccinated person without immunity is the same as that for an unvaccinated person. Let's assume this probability is denoted as p.

P(B|A) = p

Step 4: Calculate the Probability of Contracting Rubella (P(B))

To calculate the probability of contracting rubella, we need to consider both the vaccinated and unvaccinated populations.

The probability of contracting rubella for a vaccinated person is given by: - The probability of being vaccinated (0.3) multiplied by the probability of contracting rubella given vaccination (p).

The probability of contracting rubella for an unvaccinated person is given by: - The probability of not being vaccinated (1 - 0.3 = 0.7) multiplied by the probability of contracting rubella given no vaccination (q).

Since the probability of contracting rubella is the sum of these two probabilities, we have:

P(B) = (0.3 * p) + (0.7 * q)

Step 5: Calculate the Probability of Being Vaccinated Given Contracting Rubella (P(A|B))

Using Bayes' theorem, we can now calculate the probability of being vaccinated given contracting rubella:

P(A|B) = (P(B|A) * P(A)) / P(B)

Substituting the values we have calculated:

P(A|B) = (p * 0.3) / [(0.3 * p) + (0.7 * q)]

Please note that we do not have specific values for p and q, so we cannot provide an exact numerical answer. However, the formula above allows you to calculate the probability based on the specific values of p and q.

Remember to substitute the values of p and q with appropriate probabilities based on the context of the problem.