12.3.

(a) A complex system is made up of 100 components functioning independently. The probability that any one component will fail during the period of operation equals 0.10. In order for the entire system to function, at least 85 of the components must be working. Evaluate the probability of this.

(b) Suppose that the above system is made up of n components each having a reli- ability of 0.90. The system will function if at least 80 percent of the components function properly. Determine n so that the system has reliability of 0.95.