Question

a bag contains 6 tickets numbered 1 to 6. a person draws two tickets at random. if the sum of the numbers on the tickets drawn is even, he gets rupees 10, otherwise he loses rupees 5. show that the expectation of his gain is rupees 1

Answer 1

The expectation of his gain of rupees 10 is $\frac{1}{5}$.

Step-by-step explanation:

There are total 6 tickets from 1 to 6 according to question. We can not repeat the same ticket as it is present only 1 in the bag.

So, the outcomes of the even numbers from the bag without repeating the same ticket when they are taken 2 at a time is

          = 3 x 2 x 1

           = 6

And, the total no. of outcomes from the tickets when they are taken 2 at a time is

                = 6 x 5

                = 30

So, the expectation is

               = $\frac{6}{30}$

                = $\frac{1}{5}$