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

with the numbers 1,2,3and4(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 4if 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

Expert verified

(a) 16 possible outcomes for the situation

(b) The probabilityP(A)for getting sum5is1/4

Step by step solution

01

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

02

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 1as 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)

03

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 1,2,3and 4

04

Part (b) STEP 2: Explanation 

P(A)is the probability of getting 5as a sum

P(A)=Total outcomes with 5as a sum/Total outcomes

Total outcomes with 5as sum=4

Total outcomes=16

P(A)=4/16=1/4

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