Question

(c) How many components would be needed in the structure so that the probability the system will succeed is greater than​ 0.9999?

Answer 1

Prob. of a system can be a failure is less than (1-0.9999) = 0.0001 

now probability that the system will be failure when it has x components is 
(0.2)^x 

so, (0.2)^x < 0.0001 
or, x*log0.2 < log0.0001 
or, x > log0.0001/log0.2 [the sign changes coz log 0.2 is negative] 
or, x > 5.7227 

so, the no. of components (x) has to be 6