Question

QUESTION 5: A 4-sided die is used for some games. This die can only land on the numbers 1, 2, 3, or 4. All these outcomes are equally likely. Suppose we roll two 4-sided dice.

a. (3 pts) Write out the sample space (the set of all the ways in which the two dice could land).

b. (2 pts) What is the probability that at least one of the dice shows a 3?

c. (3 pts) Suppose we compute the sum of the two dice. What is the most likely sum? Explain.

Answer 1

Question 5

a)

Sample space = {(1, 1) (1, 2)  (1, 3)  (1, 4)

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

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

(4, 1) (4, 2) (4, 3) (4, 4)}

b)

Total number of outcomes in sample space = 16

Outcomes which shows 3 are (1,3), (2,3), (3,1), (3,2), (3,3), (3,4), (4, 3)

Number of outcomes which shows 3 = 7

probability that at least one of the dice shows a 3

= Number of outcomes which shows 3 / Total number of outcomes in sample space

= 7/16

= 0.4375

Probability that at least one of the dice shows a 3 is 0.4375

c)

Possible values of Sum of two dice are 2, 3, 4, 5, 6, 7, 8

Sum of (1,1) = 2

Sum of (1,2) and (2,1)= 3

Sum of (1,3) ,(2,2) and (3,1)= 4

Sum of (1,4) , (2, 3) ,(3, 2) and (4,1)= 5

Sum of (3,3), (2,4) and (4,2) = 6

Sum of (3,4) and (4,3) = 7

Sum of (4,4) = 8

So we can say that 5 is most likely sum.