Dan rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 15

Step-by-step explanation:

The factors of 15 are numbers that can divide even through 15 without any remainders.

  These numbers are 1, 3, 5 and 15;

When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.

          1       2             3              4             5                6

1       (1, 1)(1, 2)         (1, 3)         (1, 4)  (1, 5)          (1, 6)

2(2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6)

3(3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6)

4(4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6)

5(5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6)

6(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

The total that will give a factor of 15;

  (1, 2)  (2, 3)   (1, 4)    (2, 1)   (3, 2)      (4, 1)

Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;

  Probability of this  =   =

quit

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.