A pair of fair dice each numbered 1 to 6 is tossed. Find the probability of a score of a. Two odd numbers
b. A sum of 8 or sum of 12

1/4

1/6

Step-by-step explanation:

a) There is a 1/2 chance of rolling a odd number each time you roll it. Why? Because there are 3 odd numbers on a 6 sided die, 1,3,5. If we roll it twice, it would be 1/2 x 1/2 so a 1/4 chance

b) For it to be a sum of 8 the following combinations are possible, where the first number is rolled first and the second number is rolled second.

2,6

3,5

4,4

5,3

6,2  

For it to be 12, it must be

6,6

There are a total of 6 ways to achieve this, and there is a total of 36 possible combinations, therefore 6/36 = 1/6 chance of rolling a sum of 8 or 12

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional