Question

1. A pair of balanced dice is tossed. If X equals the total number of spots showing on the

dice, then, for k = 2, 3,...,12, find:

a. Pr(4≤X≤9)

b. Pr(4<X≤9)

c. Pr(4≤X<9)

d. Pr(4<X<9)

Answer 1

a)

cdf of sum x

x	n	p	cdf
2	1	0.027778	0.027778
3	2	0.055556	0.083333
4	3	0.083333	0.166667
5	4	0.111111	0.277778
6	5	0.138889	0.416667
7	6	0.166667	0.583333
8	5	0.138889	0.722222
9	4	0.111111	0.833333
10	3	0.083333	0.916667
11	2	0.055556	0.972222
12	1	0.027778	1

P(4<= X <= 9)

= P(X<= 9) - P(X<= 3)

= 0.83333 - 0.08333

= 0.75

b)

P(4 < X<= 9)

= P(X<= 9) - P(X<= 4)

= 0.83333 - 0.166666

= 0.66666

c. Pr(4≤X<9)

= P(X<= 8) - P(X<= 3)

= 0.72222- 0.08333

= 0.63889

d. Pr(4<X<9)

= P(X<= 8) - P(X<= 4)

=0.72222 - 0.166666

= 0.555555