Algebra

Probability

Medium

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

$\frac{3}{20}$

$\frac{13}{30}$

$\frac{1}{5}$

$\frac{2}{15}$

✅ Correct Option: 1

$P(\text{exactly two}) = P(A)P(B)P(C') + P(A)P(B')P(C) + P(A')P(B)P(C)$

$= \frac{1}{3}\cdot\frac{1}{4}\cdot\frac{4}{5} + \frac{1}{3}\cdot\frac{3}{4}\cdot\frac{1}{5} + \frac{2}{3}\cdot\frac{1}{4}\cdot\frac{1}{5}$

$= \frac{4+3+2}{60} = \frac{9}{60} = \frac{3}{20}$ .

Question 41

The probability that exactly one of them complete the task on time is

Question 43

The probability that B alone complete the task on time is:

Question 44

The probability that the task is completed on time by none of them is

Question 45

The probability that task is completed on time by at least one of them is:

The probability that exactly two of them complete the task on time is

Solution

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