Success Rate of College Grads: Probability of 1+ Job in 1 Year

[rainbow1]

A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating

 

[Evgeny.Makarov]

The probability that a graduate finds a job is $0.55$. The events that two different randomly chosen graduates find or don't find jobs are independent. This means that $P(A\cap B)=P(A)\cdot P(B)$ where $A$ and $B$ are events that the two graduates find or don't find jobs, respectively; $A\cap B$ is the event that both $A$ and $B$ hold, and $P$ is probability. I recommend finding the probability that none of the seven graduates finds a job.

Also, next time please write what you have done, what you understand and what the difficulty in solving the problem is. See forum rule #11.

 

[HOI]

The probability of "at least one" is 1 minus the probability of "none". And, since the probability of success for each is 0.55, the probability of failure is 0.45. The probability of "none" out of 7 is $$(0.45)^7$$.