A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than 8 ? Express your answer as a fraction or a decimal number rounded to four decimal places.

Probability is 21/36 = 7/12

Step-by-step explanation:

Imagine we have two dice. Let's make one die red and one die green.

Each one of those dice can come up 1, 2, 3, 4, 5, or 6.

But only a certain number of rolls have the dice adding up to less than 8. We will call a result of 'less than 8' our 'desired outcome'

If the red die is 1, the green die can be 1, 2, 3, 4, 5, or 6.    6 results

If the red die is 2, the green die can be 1, 2, 3, 4,  or 5.       5 results

If the red die is 3, the green die can be 1, 2, 3, or 4.            4 results

If the red die is 4, the green die can be 1, 2, or 3.                3 results

If the red die is 5, the green die can be 1 or 2.                     2 results

If the red die is 6, the green die can be 1.                             1  result

                                            Total: 21 ways to get 'desired outcome'

To get the probability of a event, we divide the number of ways to get the desired outcome by the number of all possible outcomes.

So how many ways can the the dice come up?

If red is 1, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

If red is 2, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

If red is 3, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

If red is 4, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

If red is 5, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

If red is 6, green can be 1, 2, 3, 4, 5, or 6.   - - >  6 ways

Total them up.

Or we could just multiply (6 ways for red) x (6 ways for green) = 36 ways

                                           Total: 36 ways to get 'all possible outcomes'

So the probability of the desired outcome is 21/36, which simplifies to 7/12

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour