if a safety switch has a 1 in 10 chance of failing, how many switches would a company want to install in order to have only a 1

Question

ratelena [41]

3 years ago

10

if a safety switch has a 1 in 10 chance of failing, how many switches would a company want to install in order to have only a 1

in million chance of them all failing at the same time

Mathematics

2 answers:

tatiyna · Answer 1 · 2021-11-25T08:09:22+03:00

tatiyna3 years ago

8 0

10^-n=10^-6

So n=6

Thus they will want to install 6 switches...

Romashka-Z-Leto [24] · Answer 2 · 2021-11-25T10:00:14+03:00

Because every individual switch has a 1/10 chance of failing, two switches will have a (1/10)*(1/10) chance of failing. Three switches will have a (1/10)*(1/10)*(1/10) chance of failing. This pattern will continue. Because $( \frac{1}{10} )^6$ equals 1/1,000,000, 6 switches will give you a 1 in 1 million chance of all failing at the same time.