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${1,2,3,4,5,6,7,8,9,10} The probability of rolling an even number on a 10 -sided die is ◻. (Type an integer or a simplified fraction.)$

$\{1,2,3,4,5,6,7,8,9,10\}$ $\newline$ The probability of rolling an even number on a $10$ -sided die is $\square$ . $\newline$ (Type an integer or a simplified fraction.)

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Probability of simple events and opposite events

Full solution

Q.

\{1,2,3,4,5,6,7,8,9,10\}

\newline

The probability of rolling an even number on a

10

-sided die is

\square

.

\newline

(Type an integer or a simplified fraction.)

Identify Total Number: Identify the total number of possible outcomes when rolling a $10$ -sided die. Since the die has $10$ sides, each with a different number from $1$ to $10$ , there are $10$ possible outcomes.
Identify Favorable Outcomes: Identify the number of favorable outcomes for rolling an even number. $\newline$ The even numbers on the die are $2, 4, 6, 8,$ and $10$ . There are $5$ even numbers.
Calculate Probability: Calculate the probability of rolling an even number. The probability $P$ of an event is given by $P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ . So, the probability of rolling an even number is $P = \frac{5}{10}$ .
Simplify Fraction: Simplify the fraction obtained in Step $3$ . $\newline$ $\frac{5}{10}$ simplifies to $\frac{1}{2}$ , since both the numerator and the denominator can be divided by $5$ .

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