A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Question

Vocaloid · Answer

Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating —> let’s consider the opposite scenario. Nobody finds a job within a year of graduating.

If the probability of one person finding a job is 57%, then the probability of them *not* finding a job is 100% - 57% or 43%.

The probability of nine people all not finding jobs is therefore (0.43)^9

However, we want the probability that at least one of them will find a job. That’s the opposite of this calculation. So the final probability is 1 - (0.43)^9