Question:
Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not.
Answer:
a. S = {12,13,14,23,24,34}
b. 1/6
c. ⅔
Step-by-step explanation:
Let S = Sample Space i.e. total possible outcomes
Given that candidates 1 and 2 are qualified and 3 and 4 are not qualified.
If two candidates are randomly selected. The list of all possible outcomes is as follows
S:{12,13,14,23,24,34}
And the number of outcomes is 6
b. What is the probability that both are qualified?
The event that both are qualified is given as {12} or {21}
From the sample space in (a) above, there's only one occurrence of {12} = 1
So, the probability is calculated as 1/6
c. What is the probability that exactly one is qualified?
The event that one one is qualified is given as {13,14,23,24}
Total = 4
Probability = 4/6
Probability = ⅔
