Question

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 6; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbolic form.

Either the numbers add to 11 or the red die shows a 1.
D ∩ B
D ∩ A
D' ∪ A
D' ∩ A
D' ∪ B

How many elements does it contain?

Answer 1

(a)(C)
`D^c \cup A`

(b)8 elements

Explanation:

Ina toss of a red and green dice, given the events:

• A: the red die shows 1;
• B: the numbers add to 6;
• C: at least one of the numbers is 3; and
• D: the numbers do not add to 11.

`D^c`=The numbers do add up to 11.

Therefore, the event: Either the numbers add to 11 or the red die shows a 1 is written as:
`D^c \cup A`

(b)

Sample Space of A={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)}

Sample Space of
`D^c`={(5,6),(6,5)}

`D^c \cup A`={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(5,6),(6,5)}

`D^c \cup A` contains 8 elements