1. The time between failures for an industrial machine is exponentially distributed with a mean of 40 days. What is the probability that a failure occurs in the next 30 days? a. 0.1288 b. 0.4469 c. 0.5276 d. 0.7253 2. In a medical study it was found that in a specic group 35% of individuals smoked, in that same group it was found that 5% smoked and had a heart condition. What is probability that an individual in this group had a heart condition given the individual smoked? 0.0003 0.0469 0.1429 0.7253 999'?\