7
11 
12 
13 
14 
15 
16 
12 
22 
23 
24 
25 
26 
13 
23 
33 
34 
35 
36 
14 
24 
34 
44 
45 
46 
15 
25 
35 
45 
55 
56 
16 
26 
36 
46 
56 
66 
The table shows the prices resulting from the throws of the dice.
a. There are 36 cells in the table and 18 of them are 25 or less. So the probability is 18/36=1/2.
b. 15 prices are odd: probability is 15/36=5/12.
8
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
10 
11 
21 
31 
41 
51 
61 
71 
81 
91 
20 
21 
22 
32 
42 
52 
62 
72 
82 
92 
30 
31 
32 
33 
43 
53 
63 
73 
83 
93 
40 
41 
42 
43 
44 
54 
64 
74 
84 
94 
50 
51 
52 
53 
54 
55 
65 
75 
85 
95 
60 
61 
62 
63 
64 
65 
66 
76 
86 
96 
70 
71 
72 
73 
74 
75 
76 
77 
87 
97 
80 
81 
82 
83 
84 
85 
86 
87 
88 
98 
90 
91 
92 
93 
94 
95 
96 
97 
98 
99 
a. There are only three cells ≤10, so probability=3%, 0.03 or 3/100.
b. We can see from the table that there are 27 cells containg 50 or less. That means there are 73 cells containing more than 50. Therefore the probability=73%, 0.73 or 73/100.
9. The lowest price is 11 cents. With 2 dice this result has a probability of 1/36. With 3 dice for this result you would need to throw three ones. But the probability is much lower, 1/216. Therefore, the customer would prefer to use two dice.
10. The possible outcomes for two signals are: (row is first light, column is second light):

2=Red (0.35) 
2=Green (0.65) 
1=Red (0.45) 
0.25 
0.45*0.65=0.2925 
1=Green (0.55) 
0.55*0.35=0.1925 
0.55*0.65=0.3575 
11a) There are 3 possibilities (assume that owning more than one dog or more than one cat counts as one dog or one cat):
i) dog(s) only
ii) dog(s) and cat(s)
iii) cat(s) only
36.5% covers i) and ii); 30.4% covers ii) and iii).
So there is an overlap of the sets of cat and dog owners.
We don't know how many households own both animals, so we cannot simply add the percentages.
11b) dog+both=36.5%; cat+both=30.4%, so dogcat=6.1%; total=dog+cat+both=66.9%both.
6.1+2cat=66.92both; 2cat=60.82both; cat=30.4both. So if 30.4% owned a cat and a dog, there would be no one who owned only a cat. 6.1% would own only a dog, and the total would be 36.5% owning a dog or cat or both. All those owning a cat would also own a dog. But 6.1% would own a dog but not a cat.