Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, 34% of the population has succumbed to the flu and died. There is a vaccine, but because the flu is extremely contagious, it spreads quite rapidly, and to date only 1 out of every 7 people have been vaccinated. Thirty-five percent of those who are not vaccinated die from the flu. Archie has just enough time to be vaccinated before he leaves. What is the probability that Archie will succumb to the flu and die while he is away? Round your answer to two decimal places.

Question

Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, 34% of the population has succumbed to the flu and died. There is a vaccine, but because the flu is extremely contagious, it spreads quite rapidly, and to date only 1 out of every 7 people have been vaccinated. Thirty-five percent of those who are not vaccinated die from the flu. Archie has just enough time to be vaccinated before he leaves. What is the probability that Archie will succumb to the flu and die while he is away? Round your answer to two decimal places.

Answer 1

To find the probability that Archie will succumb to the flu and die while he is away, we need to consider a few different probabilities and calculate their combined outcome.

First, let's calculate the probability that Archie is not vaccinated and dies from the flu. We know that 35% of those who are not vaccinated die from the flu. Therefore, the probability of Archie not being vaccinated and dying is 0.35.

Next, let's calculate the probability that Archie is vaccinated and does not die from the flu. We know that 1 out of every 7 people have been vaccinated, so the probability of Archie being vaccinated is 1/7. Since he is vaccinated, the probability of not dying from the flu is 1 - 0.35 = 0.65.

Now, let's calculate the probability of each scenario happening:
- The probability of Archie not being vaccinated and dying is 0.35.
- The probability of Archie being vaccinated and not dying is 0.65.

Since these two scenarios are mutually exclusive (he can either be vaccinated or not vaccinated), we can add their probabilities together to find the overall probability that Archie will not die from the flu while he is away:
0.35 (probability of not being vaccinated and dying) + 0.65 (probability of being vaccinated and not dying) = 1

However, we are looking for the probability that Archie will succumb to the flu and die while he is away, not the probability that he will survive. So, to find the probability that Archie will die, we subtract the probability of Archie not dying from 1:
1 - 0.65 = 0.35

Therefore, the probability that Archie will succumb to the flu and die while he is away is 0.35, or 35% (rounded to two decimal places).