Suppose two dice(one red, one green) are rolled. Consider the following events, A: the red die shows 1; B: the numbers add to 3; C: at least one of the numbers is 4; and D: the numbers do not add to 11. Express the given event in symbolic form.
D [upside down U] B
D [upside down U] B
D' U A
D' [upside down U] B
D' U B
^ answers to choose from
To express the given events in symbolic form, we can use the following notations:
- A: Event A occurs (the red die shows 1)
- B: Event B occurs (the numbers add to 3)
- C: Event C occurs (at least one of the numbers is 4)
- D: Event D occurs (the numbers do not add to 11)
Using these notations, the symbolic expressions for the given events are:
- A = "The red die shows 1" = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) }
- B = "The numbers add to 3" = { (1,2), (2,1) }
- C = "At least one of the numbers is 4" = { (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4) }
- D = "The numbers do not add to 11" = { (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), (4,5), (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) }
These are the symbolic expressions for the events A, B, C, and D respectively.