Democratic official has decided that changes in the state unemployment rate will have a major effect on her party's chance of gaining or losing seats in the state senate.
She has determined that if unemployment rises by 2 percent or more, the respective probabilities of losing more than 10 seats, losing 6 to 10 seats, gaining or losing 5 or fewer seats, gaining 6 to 10 seats, and gaining more than 10 seats are 0.25, 0.35, 0.15, 0.15, and 0.10, respectively
If unemployment changes by less than 2 percent, the respective probabilities are 0.10, 0.10. 0.15, 0.35, and 0.30.
If unemployment falls by 2 percent or more, the respective probabilities are 0.05, 0.10, 0.10, 0.40, and 0.35.
Currently this official believes that unemployment will rise by 2 percent or more with probability 0.25, change by less than 2 percent with probability 0.45, and fall by 2 percent or more with probability 0.30.
(a) If the Democrats gained seven seats, what is the probability that unemployment fell by 2 percent or more?
(b) If the Democrats lost one seat, what is the probability that unemployment changed by less than 2 percent?