# Theory of Expectation :: Problems on Throwing/Rolling Dice : Probability Distribution

No. Problems & Solutions [Click Hide/Show to display the solutions below the question]
01. A die is thrown at random. What is the expectation of number on it?
(Or) If x denotes the number of points on a die, find the expectation of x

Solution
[Expectation: 3.50 ; Variance: 2.92 ; Standard Deviation: +1.709]

02. Two unbiased dice are throws together at random. Find the expected value of the total number of points shown up.
(Or) Calculate the expected value of "x", the sum of the scores when two dice are rolled.

Solution
[Expectation: 7 ; Variance: 5.83 ; Standard Deviation: +2.412]

03. Find the mathematical expectation of the sum of points on n dice.

Solution
[Expectation: 3.5n ; Variance: 2.92n]

04. If a person gains or loses an amount equal to the number appearing when a balanced die is rolled once, according to whether the number is even or odd, how much money can be expect per game in the long run?

Solution
[Expectation: 0.50 ; Variance: 14.92 ; Standard Deviation: +3.863]

05. A six faced dice is tossed. If a prime number occurs sumeet wins that many number of rupees. But, if a non–prime number occurs he loses that many number of rupees. Determine whether the game is favourable or unfavorable to the player.

Solution
[Expectation:− 0.167 ; Variance: 15.142 ; Standard Deviation: +3.891]

06. A and B play for a prize of Rs.99. The prize is to be won by a player who first throws a ‘2’ with one die. "A" first throws, and if he fails "B" throws. and if he fails "A" again throws, and so on. Find their respective expectations.

Solution
[Expectation(A): 54 ; Expectation(B):45; Variance(A): 2,430 ; Variance(B): 2,430 ;
Standard Deviation(A): +49.3; Standard Deviation(B): +49.3]

No. Problems for Practice
01. If it rains, an umbrella sales man can earn Rs. 300 per day. If it is fair he can lose Rs. 60 per day. What is his expectation if the probability of rain is 0.3?