kurt will roll a standard 6 - sided die. what is the probability that he rolls a number less than 5?

Explanation:

Step1: Identify the total possible outcomes.

A standard 6-sided die has faces numbered 1, 2, 3, 4, 5, 6. The total number of possible outcomes is 6. $$ \text{Total Outcomes} = {1, 2, 3, 4, 5, 6} $$ $$ \text{Number of Total Outcomes} = 6 $$

Step2: Identify the favorable outcomes.

We want the probability of rolling a number less than 5. The numbers on the die less than 5 are 1, 2, 3, and 4. $$ \text{Favorable Outcomes} = {1, 2, 3, 4} $$ $$ \text{Number of Favorable Outcomes} = 4 $$

Step3: Calculate the probability.

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. $$ P(\text{number} < 5) = \frac{\text{Number of Favorable Outcomes}}{\text{Number of Total Outcomes}} $$ $$ P(\text{number} < 5) = \frac{4}{6} $$

Step4: Simplify the fraction.

Simplify the fraction $\frac{4}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. $$ \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3} $$

Answer:

$\frac{2}{3}$