Two resistors, with resistances \(R_{1}\) and \(R_{2}\), are connected in series. \(R_{1}\) is normally distributed with mean \(100 \Omega\) and standard deviation \(5 \Omega\), and \(R_{2}\) is normally distributed with mean \(120 \Omega\) and standard deviation \(10 \Omega\). Assume \(R_{1}\) and \(R_{2}\) are independent.

a. What is the probability that \(R_{2}>R_{1}\) ?

b. What is the probability that \(R_{2}\) exceeds \(R_{1}\) by more than \(30 \Omega\) ?

c. The combined resistance is \(R_{1}+R_{2}\). What is the probability that the combined resistance is less than \(200 \Omega\) ?