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

?

\newline

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

\newline

\_\_

Identify Prime Numbers: Identify the prime numbers on a $6$ -sided die. The prime numbers less than $6$ are $2$ , $3$ , and $5$ .
Calculate Favorable Outcomes: Calculate the number of favorable outcomes. There are $3$ prime numbers on a $6$ -sided die, so there are $3$ favorable outcomes.
Determine Total Possible Outcomes: Determine the total number of possible outcomes when rolling a die. There are $6$ possible outcomes ( $1, 2, 3, 4, 5, 6$ ).
Calculate Probability: Calculate the probability of rolling a prime number. The probability $P(\text{prime})$ is the number of favorable outcomes divided by the total number of possible outcomes. $P(\text{prime}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $P(\text{prime}) = \frac{3}{6}$
Simplify Fraction: Simplify the fraction. The fraction $\frac{3}{6}$ can be simplified to $\frac{1}{2}$ by dividing both the numerator and the denominator by $3$ . $\newline$ $P(\text{prime}) = \frac{1}{2}$

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