A person plays a game of tossing a coin thrice. For each head he is given Rs 2 by the organiser of the game and for each tail he has to give Rs 1.50 to the organiser. Let X denote the amount gained or lost by the person. Show that 'X' is a random variable and exhibit it as a function on the sample space of the experiment.

A bag contains 2 red and 3 black balls. One ball is drawn and then put back in the bag. The process is repeated three times. Every time the ball drawn happens to be red we say that the saw has resulted in a success. Let X denote the number of success recorded in 3 draws. show that X can be considered as random variable and exhibit it as a function one the sample space of the experiment.

A fair coin is tossed four times, and a person wins Re. 1 for each head and loses Rs 1.50 for each tail that turns up. From the sample space. calculate how many different amounts of money you can have after four tosses and the probability of having each of the these amounts.

In a dice game, a player pays a stake of Rs.1 for each throw of the dice. He receives Rs.5 if the dice shows up 3, Rs.2 if the dice shows 1 or 6, and noticing otherwise. What is the player's expected profit per throw over a long series of throws?

In order to supplement daily diet, a person wishes to take some X and Y tablets. The contenst of iron, calcium and vitamins in X and Y are given as below: The person needs atleast 18 miligrams of iron, 21 miligrams of calcium and 16 miligram of vitamins. the price of each tablet of X and Y is Rs.2 and Rs. 1 respectively. how many tablets of each should be person take in order to satisfy the above requirement at the minimum cost?

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/2,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(X=Y) is