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You roll a $6$ -sided die. $\newline$ What is $P$ (factor of $21$ )? $\newline$ 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

(factor of

21

)?

\newline

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

\newline

_____

Identify Factors of $21$ : Identify the factors of $21$ . The factors of $21$ are numbers that can divide $21$ without leaving a remainder. The factors of $21$ are $1$ , $3$ , $7$ , and $21$ .
Possible Die Outcomes: Determine which of these factors are possible outcomes when rolling a $6$ -sided die. $\newline$ The possible outcomes when rolling a $6$ -sided die are $1$ , $2$ , $3$ , $4$ , $5$ , and $6$ . From the factors of $21$ , only $1$ and $3$ are possible outcomes on a $6$ -sided die.
Calculate Probability: Calculate the probability of rolling a factor of $21$ . $\newline$ The probability $P(\text{factor of 21})$ is the number of favorable outcomes divided by the total number of possible outcomes. There are $2$ favorable outcomes ( $1$ and $3$ ) and $6$ possible outcomes in total. $\newline$ $P(\text{factor of 21}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $\newline$ $P(\text{factor of 21}) = \frac{2}{6}$
Simplify Fraction: Simplify the fraction. $\newline$ The fraction $\frac{2}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ P(factor of $21$ ) = $\frac{2 \div 2}{6 \div 2}$ $\newline$ P(factor of $21$ ) = $\frac{1}{3}$

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