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You pick a card at random. $\newline$ $1234$ $\newline$ What is $P(\text{even or less than } 4)$ ? $\newline$ Choices: $\newline$ (A) $50\%$ $\newline$ (B) $80\%$ $\newline$ (C) $100\%$ $\newline$ (D) $130\%$

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Probability of mutually exclusive events and overlapping events

Full solution

Q. You pick a card at random.

\newline

1234

\newline

What is

P(\text{even or less than } 4)

?

\newline

Choices:

\newline

(A)

50\%

\newline

(B)

80\%

\newline

(C)

100\%

\newline

(D)

130\%

Identify total cards: Identify the total number of cards and the favorable outcomes. $\newline$ There are $4$ cards numbered from $1$ to $4$ . Favorable outcomes for even numbers are $2$ and $4$ . Favorable outcomes for numbers less than $4$ are $1$ , $2$ , and $3$ .
Calculate favorable outcomes: Calculate the total number of favorable outcomes without double-counting. $\newline$ Even numbers: $2, 4$ $\newline$ Less than $4$ : $1, 2, 3$ $\newline$ Combine without repeating: $1, 2, 3, 4$ $\newline$ Total favorable outcomes = $4$
Calculate total outcomes: Calculate the probability. $\newline$ Probability = (Number of favorable outcomes) / (Total number of outcomes) $\newline$ Probability = $\frac{4}{4}$ = $1$ or $100\%$

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