Math / Discrete

QuestionSuppose two dice (one red, one green) are rolled. Consider the following events. $A$ : the red die shows $4 ; B$ : the numbers add to $2 ; C$ : at least one of the numbers is 4 ; and $D$ : the numbers do not add to 8 . Express the given event in symbolic form.
The numbers do not add to 2 . B D $D^{\prime}$ $B^{\prime}$ $B^{\prime} \cup D$
How many elements does it contain? $\square$

Studdy Solution

STEP 1

1. We have two dice: one red and one green.
2. Each die can show a number from 1 to 6.
3. We are given events $A$ , $B$ , $C$ , and $D$ with specific conditions.
4. We need to express the event "The numbers do not add to 2" in symbolic form and find how many elements it contains.

STEP 2

1. Interpret the events and their symbolic representations.
2. Express the event "The numbers do not add to 2" in symbolic form.
3. Determine the number of elements in the event.

STEP 3

Event $B$ is defined as the numbers adding to 2. This means $B = \{ (1, 1) \}$ because the only way two dice can add to 2 is if both show 1.

STEP 4

The event "The numbers do not add to 2" is the complement of event $B$ .
Symbolically, this is expressed as $B'$ .

STEP 5

To find the number of elements in $B'$ , we first find the total number of possible outcomes when rolling two dice, which is $6 \times 6 = 36$ .
Since $B$ contains only one element, $B'$ contains all the other outcomes.
Therefore, the number of elements in $B'$ is $36 - 1 = 35$ .
The number of elements in $B'$ is:
$\boxed{35}$

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