Answer:
a) If the sum of the balls is a factor of 30, eat at Joe's Place. If the sum is not a factor of 30, eat at Taco Towne.
Step-by-step explanation:
The sum table can be represented as :
      1    2    4    7    8
1 Â Â Â Â Â X Â Â 3 Â Â Â 5 Â Â Â 8 Â Â Â 9
2 Â Â Â Â Â 3 Â Â X Â Â Â 6 Â Â Â 9 Â Â 10
4 Â Â Â Â Â 5 Â Â Â 6 Â Â Â X Â Â Â 11 Â Â 12
7 Â Â Â Â Â 8 Â Â Â 9 Â Â Â 11 Â Â X Â Â Â 15
8 Â Â Â Â Â 9 Â Â Â 10 Â Â Â 12 Â Â 15 Â Â X
The Probability sum  is a factor of 30 = P(sum is  3, 5, 6, 10, 15)
= [tex]\dfrac{2}{20} +\dfrac{2}{20}+\dfrac{2}{20}+\dfrac{2}{20}+\dfrac{2}{20}[/tex]
= [tex]\dfrac{10}{20}[/tex]
= [tex]\dfrac{1}{2}[/tex]
The Probability sum less than 10 = P(sum is 3,5,8,9,6)
= [tex]\dfrac{2+2+2+4+2}{20}[/tex]
= [tex]\dfrac{3}{5}[/tex]
The probability sum is even = P( sum is 6,8,10, 12)
= [tex]\dfrac{2+2+2+2}{20}[/tex]
= [tex]\dfrac{8}{20}[/tex]
= [tex]\dfrac{2}{5}[/tex]
The probability sum is a multiple of 3 = P( sum is 3,6,9,12,15)
= [tex]\dfrac{12}{20}[/tex]
= [tex]\dfrac{3}{5}[/tex]
since the probability that is the sum of the ball is a factor of 30 is [tex]\dfrac{1}{2}[/tex] , Thus, the probability that the sum is not a factor of 30 will also be [tex]\dfrac{1}{2}[/tex] . Thus; the description that  accurately explains how a fair decision can be made in this situation is option A.
a) If the sum of the balls is a factor of 30, eat at Joe's Place. If the sum is not a factor of 30, eat at Taco Towne.
