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You roll a $6$ -sided die. $\newline$ What is $P(4 \text{ or even})$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{2}$ $\newline$ (B) $\frac{1}{9}$ $\newline$ (C) $\frac{4}{3}$ $\newline$ (D) $\frac{1}{3}$

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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(4 \text{ or even})

?

\newline

Choices:

\newline

(A)

\frac{1}{2}

\newline

(B)

\frac{1}{9}

\newline

(C)

\frac{4}{3}

\newline

(D)

\frac{1}{3}

Identify outcomes: Identify the favorable outcomes for rolling a $4$ or an even number. The even numbers on a $6$ -sided die are $2$ , $4$ , and $6$ . Since $4$ is also even, it's included in the set of even numbers. So, the favorable outcomes are $\{2, 4, 6\}$ .
Calculate favorable outcomes: Calculate the total number of favorable outcomes. There are $3$ favorable outcomes ( $2$ , $4$ , $6$ ).
Determine total outcomes: Determine the total number of possible outcomes when rolling a $6$ -sided die. There are $6$ possible outcomes ( $1, 2, 3, 4, 5, 6$ ).
Calculate probability: Calculate the probability. The probability $P(4 \text{ or even})$ is the number of favorable outcomes divided by the total number of possible outcomes. So, $P(4 \text{ or even}) = \frac{3}{6} = \frac{1}{2}$ .

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