Question

a teacher has a number cube with faces numbered 1 through 6. he will roll the number cube two times. the tree diagram shows all the possible outcomes that can result when the teacher rolls the number cube two times. each time the teacher rolls the number cube, he will record the number shown on the top face. then he will find the sum of the two numbers he records. what is the probability that sum of numbers he will record will be 8? write your answer as a fraction.

Answer 1

Step 1: Let us find the possible scenario that when the coin is tossed twice, the first toss plus the second toss would give us a sum of 8.

From the tree diagram:

If a first toss gives 1, there's no other possibility of getting a second toss that would give us a sum of 8. The highest possible value the teacher can get on the second toss is 6.

The highest possible sum is 1 + 6 = 7.

So we cannot get a sum of 8, if the teacher records a face value of 1 in the first toss.

If the teacher records 2 in the first toss, the teacher can get a sum of 8 if he tosses the coin and gets a 6 on the second toss.

2+6 = 8

(This is the first possible case for a sum of 8)

If the teacher records 3 in the first toss, the teacher can get a sum of 8 if he tosses the coin and gets a 5 on the second toss.

3+5 = 8

(This is the second possible case for a sum of 8)

If the teacher records 4 in the first toss, the teacher can get a sum of 8 if he tosses the coin and gets a 4 on the second toss.

4+4 = 8

(This is the third possible case for a sum of 8)

If the teacher records 5 in the first toss, the teacher can get a sum of 8 if he tosses the coin and gets a 3 on the second toss.

5+3 = 8

(This is the fourth possible case for a sum of 8)

If the teacher records 6 in the first toss, the teacher can get a sum of 8 if he tosses the coin and gets a 2 on the second toss.

6+2 = 8

(This is the fifth possible case for a sum of 8)

Number of cases for a sum of 8 = 5

The total possible sum of tossing a coin twice = 36

`\begin{gathered} \text{Probability that sum of numbers he will record w}ill\text{ be 8 = } \\ \frac{\text{Number of cases for a sum of 8}}{Total\text{ possible sum of tossing a coin twice}} \\ =(5)/(36) \end{gathered}`

The final answer is

`(5)/(36)`