Read the text carefully and answer the questions :
Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.
The probability that exactly one of them complete the task on time is
Answer & explanation
Correct answer: option 4
$P(A)=\frac{1}{3}, P(B)=\frac{1}{4}, P(C)=\frac{1}{5}$
P(exactly one completes) = $P(A) P(\bar{B}) P(\bar{C})+P(B) P(\bar{A}) P(\bar{C})+P(C) P(\bar{A}) P(\bar{B})$
$=\frac{1}{3} \times \frac{3}{4} \times \frac{4}{5}+\frac{1}{4} \times \frac{2}{3} \times \frac{4}{5}+\frac{1}{5} \times \frac{2}{3} \times \frac{3}{4} =\frac{12+8+6}{60}=\frac{26}{60}=\frac{13}{30}$
Option: 4