Set Theory

The set contains one element, which is 0. Therefore, the number of elements in this set is 1. Thus, the correct answer is option (2).

Step 1: Recall the definition of probability.
The probability of an event , denoted as , satisfies the condition: This means that the probability of any event is always between 0 and 1, inclusive. Step 2: Analyze the options.
Option (1) is incorrect because probability cannot be negative.
Option (2) is correct because is always between 0 and 1.
Option (3) is incorrect because probability values cannot be greater than 1.
Option (4) is incorrect because there are events with zero probability, meaning they cannot occur.
Step 3: Conclude the correct answer.
Thus, the correct answer is Option (2): Probability of an event is always between 0 and 1.

A standard die has 6 faces, numbered 1 to 6. Since 7 is not a number on the die, the probability of getting a 7 is: Thus, the probability is .

In a deck of 52 cards, there are 4 aces (one for each suit). The probability of selecting an ace is: Thus, the probability is .