a six-sided die with sides labeled 1 through 6 will be rolled once. each number is equally likely to be…

a six-sided die with sides labeled 1 through 6 will be rolled once. each number is equally likely to be rolled. what is the probability of rolling a number less than 5?\n\nwrite your answer as a fraction in simplest form.

a six-sided die with sides labeled 1 through 6 will be rolled once. each number is equally likely to be rolled. what is the probability of rolling a number less than 5?\n\nwrite your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Identify the total outcomes

The sample space for a six-sided die is $S = {1, 2, 3, 4, 5, 6}$, so $n(S) = 6$.

Step2: Identify the favorable outcomes

The numbers less than 5 are $E = {1, 2, 3, 4}$, so $n(E) = 4$.

Step3: Calculate the probability

The probability is $P(E) = \frac{n(E)}{n(S)} = \frac{4}{6}$.

Step4: Simplify the fraction

Divide the numerator and denominator by their greatest common divisor, 2. $$ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} $$

Answer:

$\frac{2}{3}$