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You roll a $6$ -sided die. $\newline$ What is $P(6 \text{ or even})$ ? $\newline$ Choices: $\newline$ (A) $20\%$ $\newline$ (B) $90\%$ $\newline$ (C) $50\%$ $\newline$ (D) $70\%$

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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(6 \text{ or even})

?

\newline

Choices:

\newline

(A)

20\%

\newline

(B)

90\%

\newline

(C)

50\%

\newline

(D)

70\%

Identify Outcomes: Identify the outcomes of a $6$ -sided die: $1, 2, 3, 4, 5, 6$ .
Define Event: Define the event of rolling a $6$ or an even number. Even numbers here are $2$ , $4$ , $6$ . Note that $6$ is included in both categories but counted once.
Count Favorable Outcomes: Count the favorable outcomes: $2, 4, 6$ . That's $3$ outcomes.
Calculate Probability: Calculate the probability: Number of favorable outcomes ( $3$ ) divided by total outcomes ( $6$ ). $\newline$ $\text{Probability} = \frac{3}{6} = 0.5 \text{ or } 50\%$

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\newline

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