Q:

Half-life Probability

When trying to answer a probability question a while back, I came upon a fundamental issue embodied by the following problem.
Suppose there is a block of 200 atoms, each with a half-life of 60 years. What is the probability that 10 or more atoms decay in a given 1-year period?

A:

Let $P(t)$ equal the number of atoms left after $t$ years. 
Then $P(t)=200*\left(\displaystyle\frac{1}{2}\right)^{\displaystyle\frac{t}{60}}$
Note that $P(1)\approx197.028041$
Let $x$ equal the probability that an atom decays after 1 year. Then $x=\displaystyle \frac{200-197.028041}{200} \approx 1.1485979\%$.
Note that this is equivalent to $1-\displaystyle\left(\frac{1}{2}\right)^{\displaystyle\frac{1}{60}}$
The probability that 10 or more atoms will decay is equal to $\displaystyle\sum_{n=10}^{200}\left(\binom{200}{n}*x^n*(1-x)^{(200-n)}\right)=1-\displaystyle\sum_{n=0}^{9}\left(\binom{200}{n}*x^n*(1-x)^{(200-n)}\right)\approx0.0124372\%$
(P.S. My math might be a little off, I am only a high school freshman)

