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You roll a $6$ -sided die. $\newline$ What is $P(1$ 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(1

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 $1$ or any number less than $4$ on a $6$ -sided die.
Identify favorable outcomes: Step $2$ : Identify the favorable outcomes. $\newline$ The numbers less than $4$ are $1$ , $2$ , and $3$ . So, the favorable outcomes are \{ $1$ , $2$ , $3$ \}.
Calculate total outcomes: Step $3$ : Calculate the total number of outcomes. $\newline$ A $6$ -sided die has $6$ possible outcomes ( $1$ , $2$ , $3$ , $4$ , $5$ , $6$ ).
Calculate probability: Step $4$ : Calculate the probability. $\newline$ The probability $P(1 \text{ or less than } 4)$ is the number of favorable outcomes divided by the total number of outcomes. $\newline$ $P(1 \text{ or less than } 4) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ $\newline$ $P(1 \text{ or less than } 4) = \frac{3}{6} = 0.5$ or $50\%$

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