Lucy rolls 2 fair dice and adds the results from each. work out the probability of getting a total of 10

The probability of obtaining the sum of 10 is 1/12 or 0.0833

Step-by-step explanation:

Given

2 fair dice

Required

Probability of obtaining the sum of 10

To solve this, we have to list out the sample space.

Sample space is the total possible sum that can be obtained when she rolls the dice.

Let the first die be represented with S1 and the second be represented with S2.

S1 = {1,2,3,4,5,6}

S2 = {1,2,3,4,5,6}

To get the sample space, we have to add individual elements of S1 and S2.

This is done as follows.

When S1 = 1 and S2 = {1,2,3,4,5,6}

Sum = 1+1, 1+2, 1+3, 1+4, 1+5, 1+6

Sum = 2, 3, 4, 5, 6, 7

When S1 = 2 and S2 = {1,2,3,4,5,6}

Sum = 2+1, 2+2, 2+3, 2+4, 2+5, 2+6

Sum = 3,4,5,6,7,8

Using the same pattern as used above

When S1 = 3 and S2 = {1,2,3,4,5,6}

Sum = 4,5,6,7,8,9

When S1 = 4 and S2 = {1,2,3,4,5,6}

Sum = 5,6,7,8,9,10

When S1 = 5 and S2 = {1,2,3,4,5,6}

Sum = 6,7,8,9,10,11

When S1 = 6 and S2 = {1,2,3,4,5,6}

Sum = 7,8,9,10,11,12

Writing out the Sum, will give us the sample space.

Sample Space = {2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12}

The sample space has a total of 36 elements

To calculate the probability of obtaining the sum of 10,

We have to count the number of 10's in the sample space

Number of 10 = 3

Probability = Number of 10 / Number of Sample Space

Probability = 3 / 36

Probability = 1/12

Probability = 0.0833

Hence, the probability of obtaining the sum of 10 is 1/12 or 0.0833

c

step-by-step explanation:

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.