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Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, 21% 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 16 out of every 20 people have been vaccinated. Thirty-seven 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

Answer :

Answer:

The probability that Archie will succumb to the flu and die while he is away is 17%.

Step-by-step explanation:

From the question, we have the following:

P(d) = probability of debt = the population has succumbed to the flu and died = 21%, or 0.21

P(v) = probability of getting vaccinated = 16 out of every 20 people = 16 / 20 = 0.80

P(v') = probability of not got vaccinated = 1 - P(v) = 1 - 080 = 0.20

P(d|v') = probability of not vaccinated and die from the flu = 37%, or 0.37

P(d|v) = probability that Archie will succumb to the flu and die while he is away = ?

This can therefore be estimated using the following equation:

P(d) = [P(d|v) * P(v)] + [P(d|v') * P(v')] ...................... (1)

Substitute the values into equation (1) and solve for P(d|v), we have:

0.21 = [P(d|v) * 0.80] + [0.37 * 0.20]

0.21 = [P(d|v) * 0.80] + 0.074

P(d|v) * 0.80 = 0.21 - 0.074

P(d|v) * 0.80 = 0.136

P(d|v) = 0.136 / 0.80

P(d|v) = 0.17, or 17%

Therefore, the probability that Archie will succumb to the flu and die while he is away is 17%.

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