Danita is playing a board game that involves rolling two fair dice. In this game, rolling double sixes is called "scoring a dragon." What is the complement of the event "scoring a dragon"?
A. rolling no sixes
B. rolling no sixes
C. rolling one or fewer sixes
D. rolling one or fewer sixes
rolling exactly one six
rolling exactly one six
rolling one or more sixes
rolling one or more sixes
Here are the answer choices
A. rolling no sixes
B. rolling one or fewer sixes
C. rolling exactly one six
B. rolling one or more sixes
The complement of the event "scoring a dragon" is the event of not scoring a dragon, which is rolling anything other than double sixes.
So, the answer is A. rolling no sixes.
To find the complement of an event, we need to determine what outcomes are not included in the event. In this case, we are looking for the complement of the event "scoring a dragon", which means we want to find the outcomes where double sixes are not rolled.
To do this, we can first calculate the probability of rolling double sixes. Since there are 6 possible outcomes for each dice roll, the total number of possible outcomes when rolling two fair dice is 6 * 6 = 36. Out of the 36 possible outcomes, there is only one outcome where both dice show six, which is double sixes.
Therefore, the probability of scoring a dragon is 1/36.
Now, to find the complement of scoring a dragon, we need to calculate the probability of any outcome where double sixes are not rolled. This includes rolling no sixes, rolling exactly one six, or rolling one or fewer sixes.
Out of the 36 possible outcomes, we can consider the following cases:
1. Rolling no sixes: There are 5 possible outcomes for each dice roll where a six is not rolled. Therefore, the total number of outcomes without any sixes is 5 * 5 = 25.
2. Rolling exactly one six: There are a few ways to get exactly one six:
- First dice shows a six, second dice shows any number other than six: 1 * 5 = 5 outcomes
- First dice shows any number other than six, second dice shows a six: 5 * 1 = 5 outcomes
Therefore, the total number of outcomes with exactly one six is 5 + 5 = 10.
3. Rolling one or fewer sixes: This includes the previous cases of rolling no sixes and rolling exactly one six. Therefore, the total number of outcomes with one or fewer sixes is 25 + 10 = 35.
So, the complement of the event "scoring a dragon" is rolling one or fewer sixes. Therefore, the answer is option D: rolling one or fewer sixes.