Question

Four-sided dice A four-sided die is a pyramid whose four faces are labeled

with the numbers $1,2,3$and$4$(see image). Imagine rolling two fair, four-sided dice and

recording the number that is showing at the base of each pyramid. For instance, you would

record a $4$if the die landed as shown in the figure.

a. Give a probability model for this chance process.

b. Define event A as getting a sum of $5$. Find P(A).

Short answer

(a) 16 possible outcomes for the situation

(b) The probability$P\left(A\right)$for getting sum$5$is$1/4$

Step-by-step solution

Part (a) Step 1: Given information

We have been given a four-sided die is a pyramid whose four faces are labeled with the numbers $1,2,3,$and $4$

Part (a) STEP 2: Explanation

Two fair 4-sided dices is rolled and we assume that all sixteen possible outcomes are equally likely.

The possible outcomes can be deduced by making combinations of different faces with a particular face.

For eg: Take $1$as the first face and make combinations of it with all the remaining faces.

Rolling two four-sided dice, the conceivable outcomes are:

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

Part (b) STEP 1: Given information

We have been given a four-sided die is a pyramid whose four faces are labeled with the numbers $1,2,3$and $4$

Part (b) STEP 2: Explanation 

$P\left(A\right)$is the probability of getting $5$as a sum

$P\left(A\right)=$Total outcomes with $5$as a sum$/$Total outcomes

Total outcomes with $5$as sum=$4$

Total outcomes=$16$

$P\left(A\right)=4/16=1/4$