Probability question with percentages

#1
- You are given a number of transmission switches that are unreliable in the following sense: when triggered by a sudden voltage pulse, they will close and transmit the voltage only about 90 percent of the time. Design a system, using a minimum number of these switches that will transmit some signal at least 99.99 percent of the time that a triggering voltage pulse is put into the input.

So this seems to be a binomial distribution with success p=0.9; failure 1-p=0.1; The observed probability is 0.999 but I am having trouble defining what value to assign to x in order to solve for n. Below is what I'm trying to work out....

0.999 = (n choose x) 0.9^x (1-0.9) ^ n-x
 

Mean Joe

TS Contributor
#2
You're close.

1-0.9999 = (n choose x) 0.9^x (1-0.9) ^ n-x

With this setup, x is the number of switches that succeed. So take x=0.