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You roll a $6$ -sided die. $\newline$ What is $P(\text{factor of } 24)$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Theoretical probability

Full solution

Q. You roll a

6

-sided die.

\newline

What is

P(\text{factor of } 24)

?

\newline

Simplify your answer and write it as a fraction or whole number.

\newline

_____

Identify Factors of $24$ : Identify the factors of $24$ . Factors of $24$ are $1$ , $2$ , $3$ , $4$ , $6$ , $8$ , $12$ , and $24$ .
Determine Possible Outcomes: Determine which of these factors are possible outcomes when rolling a $6$ -sided die. $\newline$ The $6$ -sided die has sides numbered $1$ through $6$ . Therefore, the factors of $24$ that are possible outcomes on the die are $1$ , $2$ , $3$ , $4$ , and $6$ .
Calculate Probability: Calculate the probability of rolling a factor of $24$ . The probability $P(\text{factor of 24})$ is equal to the number of favorable outcomes (which are the factors of $24$ that can be rolled) divided by the total number of possible outcomes (which is $6$ for a $6$ -sided die). $P(\text{factor of 24}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $P(\text{factor of 24}) = \frac{5}{6}$

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