Question

For a special game Don has two 8-sided fair dice numbered from 1 to 8 on the faces. Just as with ordinary dice, Don rolls the dice and sums the numbers that appear on the top face, getting a sum from 2 to 16. What is the sum of the possible numbers which have a probability of 1/32 of appearing

Answer 1

Answer

The sum of the possible numbers are {(1,2), (2,1)}

Step-by-step explanation:

Probability for rolling two dice with the eight sided dots are 1, 2, 3, 4, 5, 6, 7 and 8 dots in each die.  

When two dice are rolled or thrown simultaneously, thus number of event can be $8^{2}$= 64 because each die has 1 to 8 numbers on its faces. Then the possible outcomes of the sample space are shown in the pdf document below .  

As Don rolls the dice and sums the number that appear on the top face, he gets a sum from 2 to 16.

Assuming; getting sum of 2  

Let E$_{1}$ = event of getting sum of 2

E$_{1}$ = { (1 , 1 ) }

Therefore, Probability of getting sum of 2 will be;  

P ( E$_{1}$ ) = $\frac{Number of favorable outcome}{Total number of possible outcome}$

= $\frac{1}{64}$

GETTING SUM OF TWO ( i.e  { (1 , 1 ) }  ) will give the probability of 1/64 of appearing. But we are looking for the probability of 1/32 of appearing. Let look at the possibility of getting sum of 3.

Assuming; getting sum of 3

Let E$_{2}$ = event of getting sum of 3

E$_{2}$ = { (1 , 2 ) (2 , 1) }

Therefore, Probability of getting sum of 3 will be;  

P ( E$_{2}$ ) = $\frac{Number of favorable outcome}{Total number of possible outcome}$

= $\frac{2}{64}$

= $\frac{1}{32}$

For all probability of getting the sum greater than 3 to 16 will be void because there wont be a chance for 1/32 to appear. Therefore, the sum of the possible numbers are: {(1,2), (2,1)}  which have a probability of 1/32 of appearing.

I hope this comes in handy at the rightful time!