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 two of them complete the task on time is
Answer & explanation
Correct answer: option 1
P(exactly two complete)
$=P(A) P(B) P(\bar{C})+P(B) P(C) P(\bar{A})+P(A) P(C) P(\bar{B})$
$=\frac{1}{3} \times \frac{1}{4} \times \frac{4}{5}+\frac{1}{4} \times \frac{1}{5} \times \frac{2}{3}+\frac{1}{3} \times \frac{1}{5} \times \frac{3}{4} =\frac{4+2+3}{60}=\frac{9}{60}=\frac{3}{20}$
Option: 1