Question

Consider the sample space given below. A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray, 5 = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66) a) Let E be the event that the sum of the numbers showing face up is equal to 6. Write E as a set. (Write your answer in set-roster notation.) b)What is the probability of e? c) Let F be the event that the sum of the numbers showing face up is at most 4. Write Fas a set. (Write your answer in set-roster notation. ) d) What is the probability of F? Show all work in either the answer box shown or upload your answer with a file - can be PDF or jpeg only. Choose File no file selected Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display Upload File

Answer 1

Answer: a) {15, 24, 33, 42, 51} b) 5/36 c) {11, 12, 13, 21, 22, 31} d) 1/6

Explanation:

a) The set E has to contain the possible pair of numbers that show up the dice that sum up to 6. This includes 15, 24, 33, 42, 51 so the set E is

{15, 24, 33, 42, 51}

b) Since there are 5 pairs out of a possible 36, the probability that the sum of numbers that are shown face up on both sides are 6 is

5/36

c) The set F has to contain the possible pair of numbers that show up the dice that sum up to at most 4. This includes 11, 12, 13, 21, 22, 31 so the set F is

{11, 12, 13, 21, 22, 31}

d) Since there are 5 pairs out of a possible 36, the probability that the sum of numbers that are shown face up on both sides are at most 4 is 6/36 or 1/6