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

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Probability of simple events and opposite events

Full solution

Q. You roll a

6

-sided die.

\newline

What is

P(\text{odd})

?

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\%

Identify total possible outcomes: Identify the total number of possible outcomes when rolling a $6$ -sided die. $\newline$ A $6$ -sided die has $6$ faces, each with a different number from $1$ to $6$ . Therefore, there are $6$ possible outcomes when the die is rolled.
Determine favorable outcomes: Determine the number of favorable outcomes for rolling an odd number. $\newline$ The odd numbers on a $6$ -sided die are $1$ , $3$ , and $5$ . There are $3$ odd numbers, so there are $3$ favorable outcomes for this event.
Calculate probability of odd number: Calculate the probability of rolling an odd number. The probability $P$ of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. $P(\text{odd}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $P(\text{odd}) = \frac{3}{6}$
Simplify fraction for probability: Simplify the fraction to get the probability in its simplest form. $\frac{3}{6}$ simplifies to $\frac{1}{2}$ , since both the numerator and the denominator can be divided by $3$ .
Convert probability to percentage: Convert the probability to a percentage. $\newline$ To convert a fraction to a percentage, we multiply it by $100$ . $\newline$ $P(\text{odd})$ as a percentage = $(1 / 2) \times 100\%$ $\newline$ $P(\text{odd})$ as a percentage = $50\%$

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