Probability set theorem and set function( Mathematical Statistics)

e all alone 1. Consider the sample space, S, of flipping a coin 3 times and observing the outcome. i. Let the event A be at least 1 head was observed. Draw a simple Venn diagram of A. Within the circle, write all of the elements of S that are in A. Do the same for A in the same diagram. ii. Let B, be the event that the ith toss was a head. Draw a 3 way Venn diagram for the events B, B2, Bs. Make the graph big enough so you can write which elements of S correspond on the diagram as you did similarly to part i. (Make sure to put the appropriate elements in their corresponding intersections as well. For example HHH should be placed in the intersection of all 3 sets) ili. Examine the elements in A and the elements in B, BU Bs. What can we say about the two sets? iv. What does Bin Ban B, mean in words? What about Bin Bin By? Bin Bin BS? v. Using your Venn diagram, what is the relationship between Bin BinB and BUBUB