Me and a friend have a opinion difference regarding a question that got asked in a previous IT test. The short version:2 units, n and m are connected in series but operate as one system. n has a MTBF of 200, m of 300. What is the MTBF of the entire system?possible solutions:200250300500I am convinced (as is the guy who made the question) that the correct answer is 250. My friend is convinced it is 120 and the question contains a mistake. How were I to calculate this? 
MTBF calculation with 2 units connected in series
logic
If the MTBF of a device is $N$, then the probability that the device will fail in 1 time unit is $1/N$. With two devices in series with failure probabilities $p_1$ and $p_2$, the system will fail in one time unit if device 1 fails or if device 1 doesn't fail and device 2 fails. The probability of that happening is$$p_1 + (1-p_1)p_2=p_1+p_2-p_1p_2$$In your problem, $p_1=1/200, p_2=1/300$ so the probability that the system will fail in one time unit is $$(1/200)+(1/300)-(1/200)(1/300)=499/60000\approx0.00832$$and so the MTBF of the whole system is $1/0.00832\approx120.24$. Your friend is right: none of the proposed solutions are correct. 