Question

A die means a standard cube whose faces are numbered 1, ..., 6 and each has equal probability of being rolled. A green die and a red die are rolled simultaneously, with equal probability for each of the 36 possible outcomes. Describe the sample space. Then find the probability that: a. the sum is 7;

b the sum is 11;

thesumis7or11;

thesumisneither7nor11;

b. the same value occurs on each die;

c. the value on the green die is greater than 5;

d. the value on each die is less than 6;

e. the sum is even.

Answer 1

red/green	1	2	3	4	5	6
1	11	21	31	41	51	61
2	12	22	32	42	52	62
3	13	23	33	43	53	63
4	14	24	34	44	54	64
5	15	25	35	45	55	65
6	16	26	36	46	56	66

total possible outcomes =36

a) sum is 7
possible outcomes are(1,6)(2,5)(3,4)(4,3)(5,2)(6,1)

so,P(sum is 7)=6/36 = 1/6

b) sum is 11
possible outcomes are(5,6)(6,5)

so ,P(sum is 11) = 2/36

c) P(sum is 7 or 11)=P(sum is 7)+P(sum is 11) = 6/36+2/36 = 8/36 = 2/9

d)P( sum is neither 7 or nor 11 ) = 1-P(sum is 7 or 11) = 1-8/36 = 28/36 = 7/9
____________________________________________________________________________________

b. the same value occurs on each die;

possible outcomes are (11)(22)(33)(44)(55)(66)

so, probability = 6/36 = 1/6

c) value on green die will be 6 and red die can take any value
possible outcomes are = (1,6)(2,6)(3,6)(4,6)(5,6)(6,6)
P(value on green die is greater than 5)=6/36 = 1/36

d)

possible outcomes are

11	21	31	41	51
12	22	32	42	52
13	23	33	43	53
14	24	34	44	54
15	25	35	45	55

so, P(value on each die is less than 6) = 25/36

e)

possible outcomes are

11		31		51
	22		42		62
13		33		53
	24		44		64
15		35		55
	26		46		66

P(sum is even) = 18/36 = 1/2