Question

Ram, Shyam and Dev had to catch a train. Probability of catching the train by Ram
is 1/2, by Shyam is 3/4 and by dev is 2/5. What is the probability that only one of them would catch the train?​

Answer 1

Answer:

actually I think that would be 1/2×3/4×2/5 =6/40 means 3/20

Answer 2

Given:  Probability of Ram catching the train$\[ = \frac{1}{2}\]$, Probability of Shyam catching the train$\[ = \frac{3}{4}\]$, Probability of Dev catching the train$\[ = \frac{2}{5}\]$

To find: the probability that only one of them catch the train.

Solution: Find the probability of Ram not catching the train.

Probability of Ram not catching the train is $\[1 - \frac{1}{2} = \frac{1}{2}\]$

Find the probability of Shyam not catching the train.

Probability of Shyam not catching the train is$\[\begin{array}{l} 1 - \frac{3}{4}= \frac{1}{4}\end{array}\]$

Find the probability of Dev not catching the train.

Probability of Dev not catching the train is $\[\begin{array}{l} 1 - \frac{2}{5}= \frac{3}{5}\end{array}\]$

Find the probability that only one of them catch the train.

probability that only one of them catch the train$=$ P( only  Ram catches the train) + P (only Shaym catches the train) + P( Only Dev catches the train).

$\[\frac{1}{2} \times \frac{1}{4} \times \frac{3}{5} + \frac{3}{4} \times \frac{1}{2} \times \frac{3}{5} + \frac{2}{5} \times \frac{1}{2} \times \frac{1}{4} = \frac{3}{{40}} + \frac{9}{{40}} + \frac{2}{{40}}\]$

                                                        $\[ = \frac{{3 + 9 + 2}}{{40}}\]$

                                                       $\[ = \frac{{14}}{{40}}\]$

                                                        $\[ = \frac{7}{{20}}\]$

Hence, the probability that only one of them catches the train is $\[\frac{7}{{20}}\]$.