The probability that |x| is equal to a certain value can be calculated by dividing the number of favorable outcomes (where |x| equals the desired value) by the total number of possible outcomes. In this case, we need to determine the probability that |x| is equal to a specific value, given that x is chosen randomly from the set {-3, -2, -1, 0, 1, 2, 3}.

Total Number of Outcomes:
The total number of outcomes is the count of all possible values that x can take. In this case, there are 7 possible values for x: -3, -2, -1, 0, 1, 2, and 3.

Favorable Outcomes:
We need to determine the number of favorable outcomes, i.e., the number of values of x that satisfy the condition |x| equals the desired value. Let's consider each possible value for |x| separately.

1. |x| = 0:
The only value of x that satisfies this condition is 0 itself. Therefore, there is 1 favorable outcome for |x| = 0.

2. |x| = 1:
There are two values of x that satisfy this condition: -1 and 1. Therefore, there are 2 favorable outcomes for |x| = 1.

3. |x| = 2:
There are two values of x that satisfy this condition: -2 and 2. Therefore, there are 2 favorable outcomes for |x| = 2.

4. |x| = 3:
There are two values of x that satisfy this condition: -3 and 3. Therefore, there are 2 favorable outcomes for |x| = 3.

Therefore, the total number of favorable outcomes is 1 + 2 + 2 + 2 = 7.

Calculating the Probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes.

Probability = Number of Favorable Outcomes / Total Number of Outcomes

Probability = 7 / 7 = 1

Therefore, the probability that |x| equals a specific value, given that x is chosen randomly from the set {-3, -2, -1, 0, 1, 2, 3}, is 1.

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