Of all the job applicants at the Apex Company who come for a job interview ,$30$% are given the interview right away. The other $70$% are asked to wait in a waiting room. About $40$% of the time, people who are asked to wait will leave the waiting room before being given the job interview, and will not return.
(i) What percent of the job applicants who come for a job interview will actually have the interview?
I am not sure about this question. Would we have to use conditional probability or Baye's Formula for this. If so, can some someone please show me?
(ii) Given that an applicant is given an interview, what is the probability that the applicant had to wait in the waiting room?
Here is my attempt:
$P$ (given an interview right away)$*$ $P$ (had to wait in waiting room) $+$ $P$ (not given an interview right away) $*$ $P$ (did not have to wait in a waiting room)
I suppose we would have to divide this answer by the one we got in (i).
I was reading ahead about Baye's Formula and saw this question. I am not sure about part (i) and I tried on part (ii). I was thinking that we would need part (i) to use in part (ii) to get the answer. Is there a certain way I should do this? Is there a better way that I can solve this so I can see it clearer. Can someone please show me how to do this?