Question

applicants for a job first submit a written application. based on the written applications, 40% of the applicants are invited for a first interview. of those that have a first interview, 58% are rejected after the interview. what is the probability that a randomly selected applicant receives a first interview and is rejected after the interview?
0.748
0.232
0.58
0.98
0.168

Explanation:

Step1: Identify probabilities

Let $A$ be the event of getting a first - interview. $P(A)=0.4$. Let $B$ be the event of being rejected after the first - interview. Given that the probability of being rejected after the first - interview among those who have a first - interview is $P(B|A) = 0.58$.

Step2: Use multiplication rule

The multiplication rule for conditional probability is $P(A\cap B)=P(A)\times P(B|A)$.
Substitute $P(A) = 0.4$ and $P(B|A)=0.58$ into the formula: $P(A\cap B)=0.4\times0.58$.
$P(A\cap B)=0.232$.

Answer:

B. 0.232