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You roll a $6$ -sided die. $\newline$ What is $P(\text{factor of } 56)$ ? $\newline$ Write your answer as a percentage. $\newline$ $\_\_\_%$

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Theoretical probability

Full solution

Q. You roll a

6

-sided die.

\newline

What is

P(\text{factor of } 56)

?

\newline

Write your answer as a percentage.

\newline

\_\_\_%

Identify Factors of $56$ : Identify the factors of $56$ . The factors of $56$ are $1$ , $2$ , $4$ , $7$ , $8$ , $14$ , $28$ , and $56$ .
Determine Possible Outcomes: Determine which of these factors are possible outcomes when rolling a $6$ -sided die. The possible outcomes of rolling a $6$ -sided die are $1, 2, 3, 4, 5,$ and $6$ . From the factors of $56$ , only $1$ and $2$ are possible outcomes on a $6$ -sided die.
Calculate Probability: Calculate the probability of rolling a factor of $56$ . Since there are $2$ favorable outcomes ( $1$ and $2$ ) and $6$ possible outcomes in total, the probability is: $\newline$ $P(\text{factor of 56}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $\newline$ $P(\text{factor of 56}) = \frac{2}{6}$
Simplify Fraction: Simplify the fraction to its lowest terms. $\newline$ P(factor of $56$ ) = $\frac{1}{3}$
Convert to Percentage: Convert the probability to a percentage. To convert a fraction to a percentage, multiply it by $100\%$ . $P(\text{factor of } 56) = \left(\frac{1}{3}\right) \times 100\%$ $P(\text{factor of } 56) = 33.33\%$

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