Two candidates, X and Y, appeared in an interview for two vacancies for the same post. The probabilities of their selection are 1/4 and 1/7, respectively. What is the probability that one of them will be selected?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9/28
“One of them will be selected” is read here as only one: X selected and Y not, or Y selected and X not. The two selections are independent, so the probabilities in each case are multiplied, and the two cases, which cannot happen together, are added.
X not selected: \(\displaystyle 1-\frac{1}{4}=\frac{3}{4}\)
Y not selected: \(\displaystyle 1-\frac{1}{7}=\frac{6}{7}\)
Only X selected: \(\displaystyle \frac{1}{4}\times\frac{6}{7}=\frac{6}{28}\)
Only Y selected: \(\displaystyle \frac{3}{4}\times\frac{1}{7}=\frac{3}{28}\)
Only one selected: \(\displaystyle \frac{6}{28}+\frac{3}{28}=\frac{9}{28}\)
Note: With two vacancies, both X and Y can be selected, so the question can be read in two ways:
Only one of them is selected — \(\frac{9}{28}\), Option (4), the answer given by NTA
At least one of them is selected — this also counts both being selected, \(\frac{1}{4}\times\frac{1}{7}=\frac{1}{28}\), so the probability is \(\frac{9}{28}+\frac{1}{28}=\frac{10}{28}=\frac{5}{14}\), Option (3)