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You pick a card at random. $\newline$ $3456$ $\newline$ What is $P(3 \text{ or less than } 6)$ ? $\newline$ Write your answer as a percentage. $\newline$ $\_\_\_\_\%$

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Probability of mutually exclusive events and overlapping events

Full solution

Q. You pick a card at random.

\newline

3456

\newline

What is

P(3 \text{ or less than } 6)

?

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\%

Identify total outcomes: Step $1$ : Identify the total number of outcomes. $\newline$ Since the card numbers are not specified beyond the number $3456$ , we assume the cards are numbered from $1$ to $3456$ . $\newline$ Total number of outcomes = $3456$ .
Determine favorable outcomes: Step $2$ : Determine the favorable outcomes. $\newline$ The problem asks for the probability of picking a card numbered $3$ or less than $6$ . This includes numbers $1$ , $2$ , $3$ , $4$ , and $5$ . $\newline$ Favorable outcomes = $5$ .
Calculate probability: Step $3$ : Calculate the probability. $\newline$ Probability (P) = Number of favorable outcomes / Total number of outcomes $\newline$ $P = \frac{5}{3456}$
Convert to percentage: Step $4$ : Convert the probability to a percentage. $\newline$ Percentage = $(\text{Probability} \times 100)\%$ $\newline$ Percentage = $\left(\frac{5}{3456}\right) \times 100$ $\newline$ Percentage = $0.1447\%$

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