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You roll a $6$ -sided die. $\newline$ What is $P(2 \text{ or less than } 4)$ ? $\newline$ Choices: $\newline$ (A) $20\%$ $\newline$ (B) $70\%$ $\newline$ (C) $40\%$ $\newline$ (D) $50\%$

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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(2 \text{ or less than } 4)

?

\newline

Choices:

\newline

(A)

20\%

\newline

(B)

70\%

\newline

(C)

40\%

\newline

(D)

50\%

Understand the problem: Step $1$ : Understand the problem. $\newline$ We need to find the probability of rolling a $2$ or any number less than $4$ on a $6$ -sided die. This includes the numbers $1$ , $2$ , and $3$ .
Calculate favorable outcomes: Step $2$ : Calculate the total favorable outcomes. $\newline$ There are $3$ favorable outcomes ( $1$ , $2$ , $3$ ).
Calculate possible outcomes: Step $3$ : Calculate the total possible outcomes. $\newline$ A $6$ -sided die has $6$ possible outcomes ( $1$ through $6$ ).
Calculate probability: Step $4$ : Calculate the probability. $\newline$ Probability $P$ = Number of favorable outcomes / Total possible outcomes = $\frac{3}{6}$ = $0.5$ .
Convert to percentage: Step $5$ : Convert the probability to a percentage. $P = 0.5 \times 100\% = 50\%$ .

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