Binominal vs Geometric.....confused!!!!

Hi there, I am currently working on these questions but I don't really get how to work them out. Is it wrong to use the binomial distribution for a) and where is the difference between binomial and geometric? Why can't I use the binomial for the second one?

3)a) In the novel Bomber it is argued that a World War II pilot had a 2% chance of being shot down on each mission. The author claimed that a pilot was mathematically certain to be shot down by the time he reached 50 missions. Is this a valid argument?

b) Suppose that once a pilot has been downed that he is either killed or captured. Suppose that the length of his flying career is a geometric random variable. The probability of termination of the career on a mission is 0.02. Calculate the probability that he will survive 50 missions.

Thank you!