An experiment involves tossing a pair of dice (one green and one red), and recor

Question

An experiment involves tossing a pair of dice (one green and one red), and recording the numbers that come up. If x equals the outcome on the green die and y the outcome on the red die. a) Describe the sample space by listing the elements (x, y): b) List the elements corresponding to the event A that the sum is greater than 8: c) List the elements corresponding to the event B that a 2 occurs on either die: (including more 2s) d) List the elements corresponding to the event C that a number greater than 4 comes up on the green die: e) List the elements corresponding to the event A Intersection C f) List the elements corresponding to the event A Intersection B: g) List the elements corresponding to the event B Intersection C: h) Construct a Venn diagram to illustrate the intersections ad unions of the events A, B, and C

Explanation / Answer

(According to Chegg policy only four subquestions will be answered. Please post the remaining in another question)

a) The sample space for this experiment is the set of all pairs of (x,y) possible. This is shown below:

Sample space is

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

b) The sum on the two dice is greater than 8. The elements of the event are given below:

A = {(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)}

c) The event of a 2 occuring on either die is given below:

B = {(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)}

d) Since the number on the green die is greater than 4, the only values for x are 5 and 6. On the other hand, y can take any value. The event is given below:

C = {(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

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