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# Probability Problem

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Supose a pill exists with the property that one out of every 100 such pills contains a lethal amount of a substance, and that the other 99 are harmless. Caluclate how many people would be expected to die if 1,000 people each take 1 pill and if 1,000 people each take 10 pills. If 1,000 people take a single pill we would expect 10 of them to die. If the dose is 10 times as great (10 pills per person) about 95.6 or 97 people will die. I have calculated what the expected number of deaths would be if 1,000 people each took 50 pills (about 40 die), 100 pills (about 63 die) and 500 pills (about 93 die). Is that correct and how does the linear hypothesis (LH) break down at large doeses of spiked pills? Assuming the LH is correct for low doses of radiation, why is it likely to break down at very large radiation doses?

The way I did the calculations was:
For 10 pills:
(0.99)^10 = 0.9044
1-0.9044 = 0.956
95.6 people

For 50 pills:
(0.99)^50 = 0.605
1-0.605 = 0.395
Which gives me 39.5 people. That is the way that my book figured it out for 10 people. I just did to the 50th power instead of to the 10th power. Am I not doing it correct?