Question

Please use the The Law of Total Proabilities to Solve. Please round to two decimal places.

Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, 30% 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 10 out of every 12 people have been vaccinated. Forty 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. (If necessary, consult a list of formulas.)

Answer 1

From the law of total probability

$\frac{2}{12}*0.4 + \frac{10}{12}*p=0.30$

$\frac{2*0.4 + 10*p}{12}=0.3$

solving for p

$p=\frac{0.3*12 -2*0.4}{10}=0.28$

Therefore, probability that Archie will succumb to the flu and die while he is away = 0.28