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You roll a $6$ -sided die. $\newline$ What is $P(\text{factor of } 90)$ ? $\newline$ 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 } 90)

?

\newline

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

\newline

\_\_

Identify Factors of $90$ : Identify the factors of $90$ . $\newline$ Factors of $90$ are numbers that can divide $90$ without leaving a remainder. The factors of $90$ are $1$ , $2$ , $3$ , $5$ , $6$ , $9$ , $10$ , $15$ , $18$ , $30$ , $2$ $0$ , and $2$ $1$ .
Determine Possible 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 list of factors of $90$ , the numbers $1$ , $2$ , $3$ , $5$ , and $6$ are also possible outcomes on the die.
Calculate Probability: Calculate the probability of rolling a factor of $90$ . The probability $P(\text{factor of 90})$ is the number of favorable outcomes (rolling a factor of $90$ ) divided by the total number of possible outcomes (rolling any number from $1$ to $6$ ). $P(\text{factor of 90}) = \frac{\text{Number of favorable outcomes (factors of 90 on the die)}}{\text{Total number of possible outcomes (sides on the die)}}$ $P(\text{factor of 90}) = \frac{5}{6}$

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