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You pick a card at random. $\newline$ $123$ $\newline$ What is $P(2$ or less than $3)$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{4}$ $\newline$ (B) $\frac{2}{3}$ $\newline$ (C) $1$ $\newline$ (D) $\frac{2}{1}$

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Probability of mutually exclusive events and overlapping events

Full solution

Q. You pick a card at random.

\newline

123

\newline

What is

P(2

or less than

3)

?

\newline

Choices:

\newline

(A)

\frac{1}{4}

\newline

(B)

\frac{2}{3}

\newline

(C)

1

\newline

(D)

\frac{2}{1}

Identify Total Outcomes: Identify the total number of possible outcomes and the favorable outcomes. Since the problem mentions picking a card, we assume a standard deck of $52$ cards. However, the problem statement is unclear about the type of cards, so we assume it's about numbers $1$ to $4$ , making $4$ possible outcomes.
Define Event: Define the event ＂ $2$ or less than $3$ ＂. This includes the numbers $1$ and $2$ . There are $2$ favorable outcomes ( $1$ and $2$ ).
Calculate Probability: Calculate the probability using the formula $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ . Here, $P(2 \text{ or less than } 3) = \frac{2}{4} = \frac{1}{2}$ .

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