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?

If a dice is thrown 3 times in succession. What is the probability that all throws shows 6?

Find the probability of throwing a total of 8 in a single toss of a pair dice given that each dice shows up an odd number.

For a biased dice, the probabilities of the different faces to turn up are the dice is tossed and it is told that either the face 1 or face 2 has shows up, then the probability that it is face 1 is

Let two fair six-faced dice A and B be thrown simltaneously. If E_(1) is the event that die A shows up four, E_(2) is the event that die B shows up two and E_(3) is the event that the sum of numbers on both dice isodd, then which of the following statement is NOT True ?

(Rolling of a pair of dice) : Suppose your teacher challenges you to the following guessing game: She would throw a pair of dice. Before that you need to guess the sum of the numbers that show up on the dice. For every correct answer, you get two points and for every wrong guess you lose two points. Whal numbers would be the best guess?

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 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 die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws : : What is the probability that the total score is : at least 6 ?

A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws : : What is the probability that the total score is : even ?

A manufacturing company makes two types of teaching aids A and B of Maths for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hour for fininshing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for fininshing. For fabricating and finishing , the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 80 and each type of A and Rs 120 on each type of B. How many pieces of type A and type B should be manufactured per week to realise a maximum profit? What is the maximium profit per week?