a. The sample space of the 38 possible outcomes in roulette consists of the numbers 1 through 36, a 0, and a 00.
b. P(red) is the probability of the ball landing on a red number. In a standard roulette wheel, there are 18 red numbers out of the total 38 numbers. Therefore, P(red) = 18/38.
c. P(-1st 12-) is the probability of the ball landing on a number in the first dozen (numbers 1-12). In a standard roulette wheel, there are 12 numbers in the first dozen out of the total 38 numbers. Therefore, P(-1st 12-) = 12/38.
d. P(even number) is the probability of the ball landing on an even number. In a standard roulette wheel, there are 18 even numbers out of the total 38 numbers. Therefore, P(even number) = 18/38.
e. No, getting an odd number is not the complement of getting an even number. The complement of an event A is the event that A does not occur. In this case, the complement of getting an even number would be getting an odd number. The two events are mutually exclusive, meaning they cannot occur at the same time, but they are not complements of each other.
f. Two mutually exclusive events in roulette could be:
- The ball landing on a red number and the ball landing on a black number.
- The ball landing on an even number and the ball landing on an odd number.
g. The events Even and 1st Dozen are not independent in roulette. The occurrence of one event (e.g., getting an even number) affects the probability of the other event (e.g., landing in the 1st Dozen). The probabilities of these events are dependent on each other because the roulette wheel is structured in a specific way.