In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

Step-by-step solution

Probability of success i.e. getting a 5 or 6 = P s = 2 6 = 1 3 . So, probability of failure i.e. getting any number other than 5 or 6 = P f = 1 - P s = 1 - 1 3 = 2 3 . Let X be the amount that a man wins in a maximum of three throws. So, X can take values : Case I : First two throws are 5 or 6 , game stops ⇒ X = 100 ⇒ P X = 100 = 1 3 Case II : First throw is other than 5 or 6 and second and third throws are 5 or 6 , game stops ⇒ X = 50 ⇒ P X = 50 = 2 3 × 1 3 = 2 9 Case III : First two t