Question

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 2; B: the numbers add to 5; C: at least one of the numbers is 2; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.] At least one of the numbers is 2, or the numbers add up to 5. C ∪ B

Answer 1

Answer:

$C \cup B =[(x,y),:x=2 \:Or\: y=2 \:Or\: x+y=5, 1 \leq x \leq 6,1 \leq y \leq 6 ]$

Step-by-step explanation:

Let the outcome from the two dice be (x,y) where x is the outcome from the red die and y is the outcome from the green die.

Event A: the red die shows 2

$A=[(x,y), x=2,1 \leq y \leq 6 ]$

Event B: the numbers add to 5

$B=[(x,y),:x+y=5, 1 \leq x \leq 6,1 \leq y \leq 6 ]$

Event C: at least one of the numbers is 2;

$C=[(x,y),:x=2 \quad Or \quad y=2, 1 \leq x \leq 6,1 \leq y \leq 6 ]$

Event D: the numbers do not add to 9;

$D=[(x,y),:x+y\neq 9, 1 \leq x \leq 6,1 \leq y \leq 6 ]$

Therefore:

$C \cup B =[(x,y),:x=2 \:Or\: y=2 \:Or\: x+y=5, 1 \leq x \leq 6,1 \leq y \leq 6 ]$