The modulas of any number is always positive even when the number inside is negative. So [x] = -3, -2, -1, 0, 1, 2, 3 Total number =11 P[x] = 7/11

Probability Calculation for |x| < />

To find the probability that |x| is smaller than 4, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Total Number of Possible Outcomes:
The given set of numbers consists of -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5. Therefore, there are a total of 11 numbers in the set.

Number of Favorable Outcomes:
To determine the number of favorable outcomes, we need to identify the numbers that satisfy the condition |x| < 4.="" this="" means="" that="" the="" absolute="" value="" of="" x="" should="" be="" less="" than="" 4.="" />

The numbers that satisfy this condition are: -3, -2, -1, 0, 1, 2, and 3. Hence, there are 7 favorable outcomes.

Probability Calculation:
The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Therefore, the probability of |x| < 4="" is="" calculated="" />
P(|x| < 4)="Number" of="" favorable="" outcomes="" total="" number="" of="" possible="" />

Substituting the values, we get:
P(|x| < 4)="7" />

Simplifying the fraction, we find that the probability is:
P(|x| < 4)="7/11" or="" approximately="" />

Hence, the probability that |x| is smaller than 4 is approximately 0.6364 or 63.64%.

Summary:
- The total number of possible outcomes is 11, as there are 11 numbers in the given set.
- The numbers satisfying the condition |x| < 4="" are="" -3,="" -2,="" -1,="" 0,="" 1,="" 2,="" and="" 3,="" resulting="" in="" 7="" favorable="" />
- The probability of |x| < 4="" is="" equal="" to="" the="" number="" of="" favorable="" outcomes="" divided="" by="" the="" total="" number="" of="" possible="" />
- Therefore, the probability is 7/11 or approximately 0.6364, which translates to 63.64%.