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

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Probability of mutually exclusive events and overlapping events

Full solution

Q. You roll a

6

-sided die.

\newline

What is

P(\text{odd or even})

?

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\%

Identify total outcomes: Step $1$ : Identify the total outcomes when rolling a $6$ -sided die. $\newline$ There are $6$ faces on the die, numbered $1$ through $6$ . Each number represents one outcome. $\newline$ Total outcomes $= 6$
Determine favorable outcomes: Step $2$ : Determine the number of favorable outcomes for rolling either an odd or even number. $\newline$ Odd numbers on the die: $1$ , $3$ , $5$ ( $3$ outcomes) $\newline$ Even numbers on the die: $2$ , $4$ , $6$ ( $3$ outcomes) $\newline$ Total favorable outcomes for odd or even = $3$ (odd) + $3$ (even) = $6$
Calculate probability: Step $3$ : Calculate the probability of rolling either an odd or even number. $\newline$ Probability $P$ = (Number of favorable outcomes) / (Total outcomes) $\newline$ $P(\text{odd or even}) = \frac{6}{6} = 1$
Convert to percentage: Step $4$ : Convert the probability to a percentage. $\newline$ Percentage = Probability $\times 100\%$ $\newline$ Percentage = $1 \times 100\% = 100\%$

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