Bunuel wrote:

Tough and Tricky questions: Probability.

Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A) 16/81

B) 8/27

C) 2/3

D) 19/27

E) 65/81

Instead of using 1,000, let’s use variable t.

After day 1, (1/3)t have not survived and (2/3)t are left.

After day 2, (2/3)t x 1/3 = (2/9)t have not survived and (2/3)t x 2/3 = (4/9)t are left.

After day 3, (4/9)t x 1/3 = (4/27)t have not survived and (4/9)t x 2/3 = (8/27)t are left.

Thus, after 3 days the fraction that have not survived is (1/3)t + (2/9)t + (4/27)t = (9/27)t + (6/27)t + (4/27)t = (19/27)t.

Answer: D

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Scott Woodbury-Stewart

Founder and CEO

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