Question

After reading a recent report revealing that workplace diversity can improve the development of ideas, Quantitative Industrial (QI) decides to hire 2 recent graduates to have a better age-profile in its workforce. They interview many candidates but have settled on 5 finalists for the position. They have ranked their choices from 1 to 5.  Unbeknownst to them, each finalist has a certain probability of accepting their offer of $60,000 as the starting salary:

Candidate 1 -- 25%

Candidate 2 -- 50%

Candidate 3 -- 10%

Candidate 4 -- 0% or 100% if candidate 5 is also hired

Candidate 5 -- 50%

Suppose that the firm researches the market average and finds that on average 1 out of every 3 job offers is accepted. Therefore they expect that one of their first three candidates will accept the position. What's the likelihood that they will be correct?

Answer 1