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

?

\newline

Write your answer as a percentage.

\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 of Prime Number: Calculate the probability of rolling a prime number. The probability is the number of favorable outcomes divided by the total number of possible outcomes. $P(\text{prime}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{6}$
Simplify Fraction: Simplify the fraction. $\frac{3}{6}$ simplifies to $\frac{1}{2}$ .
Convert to Percentage: Convert the simplified fraction to a percentage. To convert a fraction to a percentage, multiply it by $100$ . $P(\text{prime})$ as a percentage = $(\frac{1}{2}) \times 100 = 50\%$

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