Draw a probability table for throwing two dice

[npellegrino]

Draw a table for throwing two dice (one red one blue). Find the probability.

1. That the sum is divisible by seven
2. The sum has factors whose sum is even
3. The sum is a composite number.

My solutions:

1. 1/6
2. 7/36
3. 31/36

Any advice would be great. Thanks in advanced.

 

[lanedance]

hi npellogrino - do you have a specific question? if you want the thinking checked - how did you get your solutions?

 

[npellegrino]

I am questioning my solution for the 2nd problem, wouldn't it be 7/11 since there are only 11 possibile sums (2,3,4,5,6,7,8,9,10,11.12) and the factor's sums are only even for (3,5,6,7,10,11,12)?

I attached my work below.

 

[npellegrino]

Also i believe the 3rd problem is 21/36

 

[lanedance]

I am questioning my solution for the 2nd problem, wouldn't it be 7/11 since there are only 11 possibile sums (2,3,4,5,6,7,8,9,10,11.12) and the factor's sums are only even for (3,5,6,7,10,11,12)?

I attached my work below.

i find the question that a little difficult to follow,but i would interpret it as base prime factors and not include 1...
sum facs fac sum
2 2 2 (even)
3 3 3 (odd)
4 2.2 4 (even)
5 5 5 (odd)
6 3.2 5 (odd)... and so on though it is open to interpretation...

in any case for the total probability you must use you matrix to determine occurrence, for above
2 has a 1/36 probability
4 has a 3/36 probability...

so the total probability will be
P(tot) = P(2) + P(4) +...