In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.

Home » In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.

CBSE | Class 12 | Maths | NCERT | Probability

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.

For the situation given in the equation, we have

Probability of getting a six in a throw of a die $=1 / 6$

Also, probability of not getting a $6=5 / 6$

Following that, there are three scenarios from which it is possible to compute the expected value of the amount that he wins:

As an example, consider the following scenario: He receives a six on his first try, and so meets the required probability be $1 / 6$

$\therefore$ Amount received by him = Rs. 1

(ii) Secondly, if he gets six on his second throw then the probability $=(5 / 6 \times 1 / 6)$

$=5 / 36$

$\therefore$ Amount received by him = – Rs. 1 + Rs. 1

$=0$

(iii) Finally, if he does not get a six in his first two throws but does get a six in his third throw, the probability of getting a six is increased. $=5 / 6 \times 5 / 6 \times 1 / 6$