Question

Q2) When rolling two regular dice,

i. Find the expected value of the difference between the two obtained numbers.

ii. What is the probability that the difference between the two numbers is greater than 3

Answer 1

Total out comes of throwing two dice is= 62=36

outcomes (xi,yi)	difeerence= I xi-yi I
1,1	0
1,2	1
1,3	2
1,4	3
1,5	4
1,6	5
2,1	1
2,2	0
2,3	1
2,4	2
2,5	3
2,6	4
3,1	2
3,2	1
3,3	0
3,4	1
3,5	2
3,6	3
4,1	3
4,2	2
4,3	1
4,4	0
4,5	1
4,6	2
5,1	4
5,2	3
5,3	2
5,4	1
5,5	0
5,6	1
6,1	5
6,2	4
6,3	3
6,4	2
6,5	1
6,6	0

now we can find the following frequency table

diference (D)	0	1	2	3	4	5
frequency (f)	6	10	8	6	4	2
probability P(D)	0.1667	0.2778	0.2222	0.1667	0.1111	0.0556

so,

E(D)= Di*P(Di)

= (0*0.1667)+(1*0.2778)+(2*0.2222)+(3*0.1667)+(4*0.1111)+(5*0.0556)  

=1.9347

so the expected value for the difference is = 1.9347 (upto four decimal)

ii) the probability of difference is greater than 3

= P(difference =4 ) + P(difference = 5)

=0.1111 + 0.0556

=0.1667 (upto four decimal)