Question

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. The probability that |x| < 2 is
$
  {\text{A}}{\text{. }}\dfrac{5}{7} \\
  {\text{B}}{\text{. }}\dfrac{2}{7} \\
  {\text{C}}{\text{. }}\dfrac{3}{7} \\
  {\text{D}}{\text{. }}\dfrac{1}{7} \\
$

Answer 1

Hint: To find the probability we find the total number of favorable outcomes. Then we find total number of possible outcomes and then use the formula for probability.The function modulus of a number k, denoted by |k| gives out only the positive values of k.

Complete step-by-step answer:
Given Data:
 x is chosen at random from the numbers -3, -2, -1, 0, 1, 2,3.

Total number of possible outcomes = 7

We have to find: Probability that |x| < 2

The value |x| < 2 gives us
⟹0 or 1.

Hence, the total number of favorable outcomes = 2

Probability = $\dfrac{{{\text{total number of favorable outcomes}}}}{{{\text{total number of possible outcomes}}}}$

Hence, Probability of | x | < 2 = $\dfrac{2}{7}$
Option B is the right answer.

Note: In order to solve this type of problem the key is to look for the perfect formula and proceed accordingly. Counting the total number of favorable outcomes and total number of possible outcomes is crucial. The function modulus of a number k, denoted by |k| gives out only the positive values of k.