Question 1172912: 5. Among the applicants to two vacant positions, three males and two female applicants
qualify for the final interview. Because of scheduling problems, only two applicants can
be interviewed immediately. The personnel manager selects these two be assigning a
numbered colored ticket to each applicant (say B1 and R1 for 1st male applicant in Blue
ticket and 1st female applicant in Red ticket, respectively), and then randomly drawing
two tickets.
(a) What is the sample space for this experiment?
(b) what is the event that at least one male is interviewed immediately?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely, let's break down this probability problem step-by-step.
**a. Sample Space**
First, let's assign labels to the applicants:
* Males: B1, B2, B3 (Blue tickets)
* Females: R1, R2 (Red tickets)
We need to find all possible pairs of applicants that can be interviewed. We can list them systematically:
* B1, B2
* B1, B3
* B1, R1
* B1, R2
* B2, B3
* B2, R1
* B2, R2
* B3, R1
* B3, R2
* R1, R2
Therefore, the sample space (S) is:
S = { (B1, B2), (B1, B3), (B1, R1), (B1, R2), (B2, B3), (B2, R1), (B2, R2), (B3, R1), (B3, R2), (R1, R2) }
**b. Event: At Least One Male is Interviewed**
Let's identify the outcomes in the sample space where at least one male is interviewed:
* (B1, B2)
* (B1, B3)
* (B1, R1)
* (B1, R2)
* (B2, B3)
* (B2, R1)
* (B2, R2)
* (B3, R1)
* (B3, R2)
Let's call this event "M".
Therefore:
M = { (B1, B2), (B1, B3), (B1, R1), (B1, R2), (B2, B3), (B2, R1), (B2, R2), (B3, R1), (B3, R2) }
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