Tedious problem, any better way? (weighted coin lands heads 3% of time)

[cenamuch]

If a weighted coin lands on heads only three percent of the time, what is the probability that the coin won’t land heads a single time when flipped 21 times?

I don't want to do (97/100)^21, that might take quite awhile

 

[barrick]

If a weighted coin lands on heads only three percent of the time, what is the probability that the coin won’t land heads a single time when flipped 21 times?

I don't want to do (97/100)^21, that might take quite awhile

Hi cenamuch,

I don't know any faster way to solve the problem. Note, however, that you don't need 20 multiplications: you can use the "square and multiply" technique.

More explicitly, you would compute the following sequence:

0.97^2
0.97^4 = (0.97^2)^2
0.97^8 = (0.97^4)^2
0.97^16 = (0.97^8)^2
0.97^21 = (0.97^16)*(0.97^4)*0.97
​

and this will give you the result with only 6 multiplications.

Of course, a scientific calculator is still faster.