The overall process takes about 6 weeks and consists of five stages:

• Stage 1: Task from site. This is a very easy stage, taking about 3 hours to complete, with a response expected within 7 days.
• Stage 2: Skype call. This is a medium-difficulty stage, lasting 1 hour, with a response expected within 2 days.
• Stage 3: Personal interview. This is a medium-difficulty stage, lasting 4 hours, with a response expected within 1 day.
• Stage 4: Home test task. This is an easy task, but time-consuming, requiring about 2 weeks to complete, with a response expected within 5 days.
• Stage 5: Another personal interview. This is a hard stage, lasting 3 hours, with a response expected the next day.

I successfully passed the first four stages but failed the fifth. I went into that interview exhausted and sick, mistakenly believing it wouldn't be too technical. Despite my frustration, it was an interesting experience.

A table has 9 boxes.

With probability $p$, the table contains a ball in one of the boxes.

You have examined 8 boxes and found no ball there.

What is the probability there is NO ball in the table?