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You roll a $6$ -sided die. $\newline$ What is $P$ (even or less than $6$ )? $\newline$ Choices: $\newline$ (A) $50\%$ $\newline$ (B) $130\%$ $\newline$ (C) $100\%$ $\newline$ (D) $80\%$

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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

(even or less than

6

)?

\newline

Choices:

\newline

(A)

50\%

\newline

(B)

130\%

\newline

(C)

100\%

\newline

(D)

80\%

Identify outcomes: Identify the total outcomes and favorable outcomes. A $6$ -sided die has numbers $1$ through $6$ . Even numbers on the die are $2$ , $4$ , and $6$ . Numbers less than $6$ are $1$ , $2$ , $3$ , $4$ , and $1$ $1$ .
Calculate union: Calculate the union of the two sets (even numbers and numbers less than $6$ ). The union set is \{ $1, 2, 3, 4, 5, 6$ \} because all numbers on the die are either even or less than $6$ .
Count outcomes: Count the number of favorable outcomes. There are $6$ numbers in the union set.
Calculate probability: Calculate the probability. Probability = Number of favorable outcomes / Total outcomes = $\frac{6}{6} = 1$ or $100\%$ .

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