You are on probation with Statisticus Ltd for 4 weeks, as sales engineer. The waiting time between sales is exponentially distributed, but with parameter \(\lambda\) being a characteristic of the salesman. The requirement for being permanently hired is 2 sales within the probation period.

(a) What is the probability of getting the first sale within 2 weeks, as a function of \(\lambda\), when time is measured in weeks?

(b) What must your \(\lambda\) be if you are going to have at least a \(60 \%\) probability of permanent employment?