Let's solve the problem step-by-step.
### Understanding the problem
A standard die has 6 faces with the numbers 1, 2, 3, 4, 5, and 6. When a die is thrown, each face has an equal probability of landing face up. Therefore, there is a total of 6 possible outcomes.
### (i) Probability of getting a 2
A die has one face showing the number 2. Therefore, there is only one favorable outcome (i.e., getting a 2) out of the total 6 possible outcomes.
[tex]\[
\text{Probability of getting a 2} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6}
\][/tex]
The result in decimal form is approximately:
[tex]\[
\text{Probability of getting a 2} ≈ 0.1667
\][/tex]
### (ii) Probability of getting a number less than 3
A number less than 3 on a die can be either 1 or 2. There are 2 favorable outcomes (i.e., getting a 1 or a 2).
[tex]\[
\text{Probability of getting a number less than 3} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3}
\][/tex]
The result in decimal form is approximately:
[tex]\[
\text{Probability of getting a number less than 3} ≈ 0.3333
\][/tex]
### (iii) Probability of getting a composite number
Among the numbers on a die (1, 2, 3, 4, 5, 6), the composite numbers are 4 and 6. Composite numbers are numbers that have more than two distinct divisors. Therefore, there are 2 favorable outcomes (i.e., getting a 4 or a 6).
[tex]\[
\text{Probability of getting a composite number} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3}
\][/tex]
The result in decimal form is approximately:
[tex]\[
\text{Probability of getting a composite number} ≈ 0.3333
\][/tex]
### (iv) Probability of getting a number not less than 4
A number not less than 4 on a die can be 4, 5, or 6. There are 3 favorable outcomes (i.e., getting a 4, 5, or 6).
[tex]\[
\text{Probability of getting a number not less than 4} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2}
\][/tex]
The result in decimal form is:
[tex]\[
\text{Probability of getting a number not less than 4} = 0.5
\][/tex]
### Summary
(i) The probability of getting a 2 is approximately 0.1667. \
(ii) The probability of getting a number less than 3 is approximately 0.3333. \
(iii) The probability of getting a composite number is approximately 0.3333. \
(iv) The probability of getting a number not less than 4 is 0.5.
