Practicing Success
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 |
$\frac{3}{20}$ $\frac{13}{30}$ $\frac{1}{5}$ $\frac{2}{15}$ |
$\frac{3}{20}$ |
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 |